If both parties reside in one State, can one of the persons sue them in a different state?

Are you asking about a small claims suit? It depends of course on the small claims rules for that state, and if the transaction or occurrence has some connection with the "forum" state.

No small claim suit. There is no connection w the state at all.

no small claim suit. there is no connection w the state at all.

Then what is this question doing in the small claims forum? :)

Anyway, you are saying that there are two persons (call them "defendants") who live in "State A", and someone ("plaintiff") wants to sue them in "State B". Defendants have no connection with "State B".

By no connection, you mean none of the following "minimal contacts" occurred?

contract giving rise to the suit was negotiated (in whole or in part) in state B.
contract was to be performed, in whole or in part, in State B.
something pertinent to the suit happened in State B.

For a full list of the possible "minimal contacts", check the "long arm statute" for State B.

No. Plaintiff cannot sue in State B.