The Ta152H was the type that is verified to have seen combat. The A and B versions could have entered production in January 1944 had the RLM not turned them down in late 1943. The Ta152 A/B versions did not offer a significant increase in performance over the FW190A currently in production to motivate the retooling of a significant portion of the aircraft industry. At least that was the reason given officially by the RLM. Clearly, they did not realize there actually was a huge increase in development potential in the Ta152 compared to the old workhorse FW190A with its huge BMW 801 radial.
In 1944 the Ta152H and C versions were granted production status. The FW190D also entered production as a stop-gap (read panic) solution (as by mid-44 the situation became outright embarrassing to the RLM) until the 152 production had started and the only significant upgrade was the inverted V12 Junkers Jumo 213A. It was significant however, we can all appreciate the difference between the Dora and the contemporary FW190A-8. The Ta152C however, may also have entered service. It was so similar to the more common FW190D that it could easily have been mistaken for it. The differences were a 50 cm longer wingspan, and a Ta152 tail, besides the DB603LA engine. This was a bit special because Kurt Tank had always wanted a Daimler-Benz to power his fighters but that production had always been reserved Messerschmitt, all DB production went to him. This was perhaps the ultimate recognition of Kurt Tank, that he finally was granted access to the DB line of production. I'd argue that had the FW190A been built with a DB engine from start, it would have shocked the RAF even more and additionally the true potential of the design had been fully realized. The BMW801 was tough alright, but the penalties of the huge frontal area can not be denied. So the Ta152C represented what Kurt Tank had always wanted to build.
It should be noted that the A/B versions (B was supposed to be Nachtjagd equipped) offered the inline potential of the Jumo 213A. For armament it had many optional setups, most notably it had MG151/20 cowling mounted (replacing the MG131s of the Dora) and was designed to carry the Mk103 center, firing through the engine and propeller hub. This was its most basic configuration, Mk103 center + 4 MG151/20s. There were also provisions for MG151/Mk108 in the outer wing stations as well as underwing pods for Mk103s. (By the way, that was the reason for Tank redesigning the whole wing and as he did so he also made it possible to detach one wing at a time making field repairs easier.) Now tell us that THAT is not a significant upgrade vs the Anton! However what probably killed it was that at the time the RLM looked at it the Jumo 213A was not offering much for power and looked weak in a comparison to the BMW801. It was not yet realized it was possible to take the Jumo beyond 2100 hp, as later Doras proved (D-11, 12, 13). The Ta152C was designed as a allround fighter/attack aircraft and had the same armament provisions as the A/B versions.
Anyway, the Ta152C may or may not have entered production and service with active units. Factory workers have testified it was in production, none are alive today. While records (those found, should be noted, because much was destroyed) show no such production. If there were any Ta152C active with front line units they could very easily have been mistaken for the more common FW190D and scrapped as such. There's supposed to have been a Ta152C equipped with a EZ42 gyroscopic sight at Rechlin which was slated for JG11 but it is unclear if it ever reached a JG11 unit, if it did it most likely would have been the JG11 Stab flight but that's remains just a guess.
Many of the Ta152H produced were lost to sabotage or airstrikes when transported on train. One Geschwaderkommodore who'd had a chance to test the Ta152H requested them for his whole Geschwader immediately and went through the roof when he heard about the production problems.
On a side note, the more-or-less famous incident when Kurt Tank left two P51Ds in the dust is likely to have been in one of the C prototypes. Tank flew both types frequently (participating in combat, unofficially) and the C had the specs to explain such a monstrous acceleration from rotation. Tank had just taken off when he heard the call from the tower that two Mustangs were 'over the fence' meaning at the very edge of the airfield, Tank engaged the emergency power system and just left the 51's behind.
The Ta152 is a interesting subject, but not without some controversy. As the situation deteriorated for the germans, proper documentation was ignored, destroyed or otherwise mishandled.