I have seen the March 1944 date posted before, but I dont beleive its correct.
For starters I will give this link that includes the service dates for all the LW day fighters in the JGs from 3/42 to 12/44:
http://www.ww2.dk/oob/bestand/jagd/bjagd.htmJG77 has the earliest entry there, for 10/44.
I have seen no book that gives a date prior to 10/44, and there are many internet sources that quote 10/44, I will leave one here, by Richard Corey, he has his sources at the bottom of the article:
http://www.yumodel.co.yu/batajnica_air_show/a_tale_of_two_me109s.htmThe 109K and 109G-10 were both delayed by the DB605D engine development, they were in fact, delivered at almost the same time, in the Fall of 1944. Both types were in service after the 109G-14.
The first large scale use of either type was "Bodenplatte" in January 1st, 1945. I dont mean 1st mission, I just mean used in significant #s.