I guess this question is more for the D&D Beyond Homebrew Items experts.

I want to custom create a Ring of Wizardry that allows the wearer to prepare a number of additional spells equal to their Intelligence modifier.

How would I go about creating that item so it works in D&D Beyond when equipped? 

To the best of my knowledge, homebrew items cannot modify the number of spells a wizard (or anyone else) can prepare.  Any item that states it can do so in the game is currently nonfunctional.  The only way I can think of to jank such an item into halfway working is deeply involved and wildly prone to player error or abuse.  Might have to give this one up as a nonthing.  Sorry, Doc.

Bummer, that sucks that D&DB doesn’t allow more customization in that area since it’s not  bad in other parts of the character sheet.

Thanks anyway.

Yurei1453 is correct. The jank workaround in question is to have them override their Wizard’s Int high enough (max 30) that their Int mod increases by the desired amount (max of +10) so that they can over prepare and then resetting their Int to the correct score. You can see why they said it was prone to error or abuse.

You can make a ring that has no function beyond text description.

You can then edit the subclass to have a hidden feature to add the spells as "always prepared", uses spell slot: yes. You can leave it for the player to select spells but you won't be able to limit to spells in their book. This will require checking they are only selecting spells they have in book and it will mean having to use the character builder to change them every time they change their spell prep involving those, or if they remove/unattune to the ring. Also needs changing if Int ever changes.

Awkward, clunky, not ideal by any means, and relies on player honesty but technically results in what you want without having to manually override your Int score every time.

Seems more trouble than it’s worth. Maybe best to just make a more powerful Pearl of Power in Ring form.

You could also just have them write down the extra spells they prepared on their character sheet's notes.

You can use a Ring of Spell Storing instead.  A wizard can cast different spells each day, no?  During downtime, just have them fill the ring with certain spells and on the adventure day, they prepare other spells.  In total, they shall have more spells available to them overall.  This can also be used to solve the Sorcerer or Warlocks limited spell issues slightly, but since their spell lists are static, it usually works out better if there is a wizard in the party and they put spells into a ring worn by the Sorcerer or Warlock.