Think of this scenario: you are running a campaign where the BBEG is a Fiend who is well known in the D&D universe (such as Asmodeus). Now in the middle of the campaign, a new player joins and decides to play a warlock - who made their patron the BBEG without knowing about it being the BBEG. How would you guys handle this?

I think this scenario would be more interesting if it was a player who had been with the group from the outset and over time it became clear their patron was the problem. Introducing a new character mid-campaign with such an obvious problem for the existing group sounds divisive to me. A good roleplaying group could of course get around that, but it just doesn't feel as compelling to me as seeing a warlock and the party as a whole come to grips with the fact they have to defeat the source of part of (or in the warlock's case most of) their power. 

This has a HUGE potential to go south in the kind of way that can destroy a campaign.  Party conflict, conflicting loyalties, and a potential to detail the campaign’s plot are all major problems that can break a campaign and spill from character conflict to table conflict.

That does not mean you cannot do something like this - and I have seen almost this exact same situation successfully pulled off at a table I DMed - but it would be very group and player specific. Unless I was comfortable my group would be cool with this as a plot, and I was certain the player would be able to pull off such a character without breaking the so I al compact of D&D, I would simply tell them “hey, listen, that’s the Big Bad, so I can’t really let you do that. But I can offer this alternative patron for the same pact.” 

This also is a problem that easily could have been avoided - when a player joins late, both the DM and the player have a bit of a responsibility to confer and make sure the new player has sufficient background about the campaign to make a character that would vibe well wirh the party and plot. If something got this far, where the player accidentally made something dedicated to the BBEG, that represents a failing of communication from both the player and DM.

New player, needs to change so it would adapt to your world.

While there are any numbers of possible work around the basic premise is leading to one one of two standard conclusions: 
1) the party gets Tpked trying to take on the bbeg as he pulls the warlock’s powers for turning on him. Or.
2) the warlock loses all his powers as the party defeats the bbeg. 
Either way the warlock loses their powers and effectively loses their levels starting over at best.

It can be a really good and engaging arc. There is an Actual Play (I won't name it to avoid spoilers) where the Patron develops into one of the BBEGs, and it's bringing up some really interesting conflicts.

The problem is twofold. As mentioned, if the Warlock turns on the Patron, how do you handle their powers which are, according to lore, dependent on the Patron's powers? My solution to that would be to have a rival Patron try and poach the Warlock. That way, if the Warlock decides to turn against their Patron, they can turn to the new one and continue being a Warlock without completely breaking lore. I'd bring this decision to a head before the finale, perhaps cost the Warlock their powers, then give them a bit of time to adjust to the new Patron (not a full campaign, maybe a quest or two) and regain full powers with the new Patron.

The other is, that it depends extremely heavily on the nature of the player in question and their relationship with the group.

Most players think they can separate themselves from the character enough to handle PvP. Most DMs want to believe that their players are like that (for various reasons), and so convince themselves it's true. In my experience, most players are not. I've had several PvPs, and barring the ones where the character was under the sway of someone or something else (eg Charmed, werewolf curse, nothic curse, etc) which helped the players categorise them as a monster rather than a player being a problem, I've only seen it work well once outside of semi-professional games.

That they seem to be a new player to the group screams at me that this is almost certainly not a good dynamic to introduce to the table. Too many unknowns and ways it could turn sour.

Last point to raise is, is this Fiend Patron known to be the BBEG? Or is it a mystery BBEG who the Warlock happened to pick out of coincidence?

If it's the former, then that's a dynamic you'll have to manage - how does a Warlock of Asmodeus (say) work in a party that is trying to overthrow (or whatever) Asmodeus? It also makes things easy for you to get out of it - just tell them having the BBEG as a Patron isn't going to work. Then suggest an alternative Fiend to work as a Patron.

If it's the latter, then you still have the above conflicts to consider. If you don't want to deal with it, you can just say that Asmodeus (or whoever) isn't accepting Warlocks at this time.

So, it can work. Mechanically, warlock powers are not dependent on the good grace of the patron. Any consequences for working against your patron are in the realms of roleplaying and DM fiat. (And the DM fiat should not be deployed without discussion with the player.) There's a perfectly valid interpretation of Warlocks where they learned arcane lore from their patron. Stealing power is another option. Also, since Asmodeus is canonically lawful, there might well be a contract that limits what he can do to the character's powers.

In any event, "warlock working at cross-purposes to their patron" is a dynamic that ought to be available.

However, if it is a problem in your opinion, you can tell the player to pick a different patron. Patron choice beyond "fiend" is a worldbuilding detail, and thus the DM must have a say. If Asmodeus doesn't exist in your world, obviously a PC can't pick it. If he's not taking warlocks, likewise. Really, the player should have been working with the DM to pick a patron that fits, and "you don't know who your patron is" is entirely valid.

One thing you want to avoid too is the story revolving too much around the patron because it in turn makes the story much more about the warlock than the rest of the party.

Been there, done that - it can work, but needs to be handled correctly. At some point that player's character is going to have to make some hard choices, and none of those choices need to be TK'ing fellow party members. You, as the DM, control the patron and what the patron demands of the warlock. Unless your campaign involved permanently slaying the patron, which in the case of a demi-god or higher is more likely to result in just the temporary slaying of the diety (they tend to come back after a while), the patron isn't likely to order the warlock to kill the party (unless YOU wanted it to happen).

You don't have to use these, but they are what i did and presented to player when such things happened.
When this cropped up for me, and boy has it at least 3 times, I would talk to the player, making sure it was overtable knowledge, and not on table, and lay out some options like.

1: Story beats where they have a chance to defy their patron, and something else steps in at an opportune moment to take their contract, giving them a different patron with interesting story associated with it to come later.

2: The wording of the contract lets them keep their power even if they defy their patron, or something like the power is theirs to do with as they please, because payment or service has already been rendered. ( I did this for someone who was from a family of Warlocks, and when their patron became a problem, the family was still paying the requisite tribute, and so power could not be revocked from the player or any of their family, since that would default the contract in the mortal's favor )

3: Patron is ammused that his own power is being used against him, and continues granting power to "Spice up the game" but this works better with more chaotic entities, or ones who are not so obsessed with law as a means of gaining an upperhand.

4: Facade Patron. The whole time, the player thought they were dealing with say, Asmodeus, but the entity granting the power was not Asmodeus and was using his name as a front for stronger bargaining.  

Derivation of 1: They break their pact in such a way they absorb part of the power they had, and it transforms them into a Sorcerer.
I used this one and the Dwarf Warlock became a Squat Tiefling with a beard made of snakes. He was disowned by his clan, even when they all saw him defy GIGASATAN on their behalf. He stuck with the party, and his player's new character motivation became proving himself despite his appearance. 

There is also the option of a not doing anything and taking the gamble that it will either get supremely ugly or lead to a memorable and spontaneous story, but I recommend against this one, because i have seen it get friendship endingly ugly. Which is why I came up with my methods of handling it to begin with.