The title says it all. I want to add an ability like rage onto my homebrew sorcerer subclass, but I don't see an obvious way to do that. What's more, I wanted to add 3 different versions the player can choose from and I don't see an obvious way to do that either. Could someone help me out?

Rage doesn’t actually “do” anything on the sheet, it’s just plain text with a limited use counter. You can make it say anything you want to, and the limited use counter is easy. Please see the Homebrew Subclasses & Species FAQ #4 for instructions as to how to set that up: (https://www.dndbeyond.com/forums/dungeons-dragons-discussion/homebrew-house-rules/131411-a-homebrewers-how-to-faq).

Ok. This was helpful, but how do I set up the two rage copycats in such a way that the player needs to choose 1 or the other since they actually have a damaging action behind them?

What exactly do you mean? I’m asking because there are different ways I might do it depending on exactly what you want. I tell ya what, it might be simpler if you just copy/paste the description of your feature into a post here so I can read it.

Ok. Here are the texts I've been using to describe them:

for 1 minute, whenever a hostile creature enters, starts, or ends their turn within 10ft of you they take 1d6 fire damage. Furthermore, you gain resistance to fire damage, and your choice of bludgeoning, piercing, or slashing (Must be announced before the resistance is applied).

Whenever a creature enters, starts, or ends their turn within 15ft of you for any reason, they take 2 cold damage. In addition, you have resistance to cold damage and your choice of bludgeoning, piercing, or slashing damage (Must be announced to the DM). Enemies affected by the cold damage of cooling rage have their movement speed reduced by 15ft. These effects last until a long rest.

What’s the text for the whole feature? Do they choose which one to use when they use it, or do they choose it when they get the feature, or at the end of every long rest or what?

Quote from MIKAIRA_ALL_TIER_GOD >>

Ok. Here are the texts I've been using to describe them:

for 1 minute, whenever a hostile creature enters, starts, or ends their turn within 10ft of you they take 1d6 fire damage. Furthermore, you gain resistance to fire damage, and your choice of bludgeoning, piercing, or slashing (Must be announced before the resistance is applied).

Whenever a creature enters, starts, or ends their turn within 15ft of you for any reason, they take 2 cold damage. In addition, you have resistance to cold damage and your choice of bludgeoning, piercing, or slashing damage (Must be announced to the DM). Enemies affected by the cold damage of cooling rage have their movement speed reduced by 15ft. These effects last until a long rest.

The only ways to implement temporary effects is by using a magic item or a feat. Using a magic item is the simpler way because of the way you can set up your inventory into sections and have a convenient equip/unequip method, whereas feats are a little more cumbersome to turn on/off. The downside of using a magic item is you don't have the ability to add an action, it's just modifiers. Here's the breakdown I'm seeing:

whenever a hostile creature enters, starts, or ends their turn within 10ft of you they take 1d6 fire damage.

This will require an action to create the rollable damage button. You'll have to make this with a feat as magic items do not have actions

Furthermore, you gain resistance to fire damage, and your choice of bludgeoning, piercing, or slashing (Must be announced before the resistance is applied).

This only needs a magic item to reproduce, though it needs 3 different magic items. One for fire and bludgeoning, one for fire and piercing, and one for fire and slashing. You'd think this could be done with a feat that has options, but feat options only give you actions based off that option, not modifiers. If you go the feat route, you'll have to make 3 different feats. Granted those 3 feats could have the 1d6 fire damage action explained above.

Whenever a creature enters, starts, or ends their turn within 15ft of you for any reason, they take 2 cold damage. 

This isn't even a rollable damage button and is strait up just text. Action text would be nice as a more convenient place for this information to be displayed, but is not absolutely necessary. 

In addition, you have resistance to cold damage and your choice of bludgeoning, piercing, or slashing damage (Must be announced to the DM). Enemies affected by the cold damage of cooling rage have their movement speed reduced by 15ft.

Similar to the fire resistance and your choice of bludgeoning, piercing, and slashing damage above where you pretty much have to make 3 different magic items (or 3 different feats) to replicate your text, you have to do the same thing here. This will give you a minimum of 6 different magic items or feats to accomplish what you want for a temporary effect.

That's all the technical advice I can give on this, though I'm confused by the "for 1 minute" at the beginning of the fire section and the "These effects last until a long rest." at the end of the cold section. So 1d6 extra damage and fire resistance lasts for a minute but 2 extra damage and cold resistance lasts till you go to sleep? I'm guessing the effects that last until a long rest is the speed reduction, it's kinda confusing so I'm not sure.

Like I said, just tell me exactly what you want it to do and I’ll tell you how I would do it.

Okay, thanks.

Okay. So if I want the player to choose one option to take and leave the other one, just follow the thing you showed me?

It depends on how you want it to behave on the character sheet. If you want it to actually apply the resistances, etc., then you might want to use the workarounds that Mairondil mentioned (but might not).

if you just want it to behave like the Rage feature does, and if they get to pick whichever one they want to use on a case-by-case basis, then you can just list everything in plain text and attach three Actions to the feature (one for the checkboxes and one for each of the pseudorages), and the player will just check off the box and do the rest manually.

If they choose their pseudorage when they gain the feature and that’s the only one they can ever use you would implement that with Options.

If you really, really want to put all the bells and whistles on, you could do it with Options and the player would just back into the character builder, select the appropriate Option, and go back to the sheet to play. Then, when the pseudo rage ends they would again back into the builder and I select the Option to turn everything off.

So, I’ll ask again:

When do they make their choice between hot and cold, when they use the feature, or when they gain the feature?

Because the answer to that👆question will determine how I explain it to you.

They get to make the choice at level 1. Starting at level 1, they are supposed to choose between hot and cold, and by choosing one, they are foregoing the other.

Cool. Then you would create a feature with two Options attached to it, one for fire and the other for cold. You can read all about how to implement Options in the Homebrew Subclasses & Species FAQ #1 (linked above). Then you would attach an Action to each option that will generate the rollable and contain the limited use tracker like explain in that FAQ.

Now, you got a choice. You can handle the resistances in one of a few ways:

1. You can simply implant them as nothing more than plain text and leave it up to the player to remember. (This is how regular Rage is implemented.)
2. You can apply the energy resistance and it will display on the player’s character sheet all the time and leave it up to the player to remember not to use it all the time. (Not recommended.)
3. You can use magic items to implement them on a temporary basis the way Mairondil suggests. (A solid choice, but it involves handling additional stuff besides just the subclass.)
4. You can do most of it with Options. You would apply the elemental resistance to the Option and the player would select/deselect the option every time they used the feature so it could handle the temporary stuff for you, but leave the B/P/S resistance as plain text that the player would have to track for themselves. (A viable option, but involves some attention on the player’s behalf.)
5. You can go all out and do it all with Options. You would create 6 Options instead of 2, one for each possible combo of elemental & B/P/S damage and the player would swap them around as necessary. (This one is the biggest pain in the ass for both you as the programmer and the player, but if the player is competent with the system then it’s the most comprehensive way to go.)

Personally, if it were me I would either go with #1 or #5 depending on how ambitious I was feeling.

Ok. Thanks. So I got the options made and decided to make the resistances just plain texts. Now all I have to do is figure out how to make them choose between two options. Because I went back and made sure the feature says "has options," and made the two options, but it's not showing up. I need to figure out what I'm doing wrong.

Check out the FAQ I linked for you, Subclasses & Species FAQ #1. It has a full walkthrough all about Options.