Question about deadlocked election

[AtorBoltox]

Ok, in an election where the EC is deadlocked and so the President must be decided by the house, if the house selected a president from one party and the senate the VP nominee from the other, could the President fire the VP and replace them with their own choice or are they constitutionally obligated to keep them for the full four year term?

[True Federalist (진정한 연방 주의자)]

He would have to keep him just as Adams had to keep Jefferson as Veep. The Constitution doesn't officially recognize any such thing as party affiliation.