From Hitchcock (Messerschmitt O-Nine Gallery), p. 101:
"The RLM advised Messerschmitt to expedite development of a high altitude fighter by incorporating Me 209H systems directly into the Bf 109H program (see p. 92). Messerschmitt complied, but continued construction of the Me 209H V1, albeit on a low priority basis. Accordingly, early in 1943 a design was advanced based on the Me P.1091a resulting in the Me 209H. Although it was not fitted to the Me 209H V1, the DB 627B [I think this should be DB628 based on other references Hitchcock makes] was selected. Delays protracted its completion until June 1944, and by this time the Me 209 and the DB 627 programs had been cancelled. Therefore, the Me 209H V1 was completed with a DB 603G (similar to the DB 627 but lacking after-cooler and two-stage mechanical supercharger)."
So, there was the Me 209 V1 through V4 (the record-breaker), with the V4 being the proposed fighter.
Then followed the Me 309
Then the revised Me 209, usually called the Me 209-II.
Then the RLM wanted a high-altitude variant of the 209-II. It sounds, though, that the 209H was really a continuation of the stretched Bf 109 program (P.1091a), and only used some systems architecture from the 209A.