The Bánhidy name is indeed represented in the nobility literature, including the coat of arms. However, no Ladislaus/László appears in the genealogies, nor any connection with Csongrád.
Marksaid is most likely a Magyarized form of a German name, also Marksajd. The German was probably something like Markscheid. I also see Markschejd in Radix. No similar name appears in the Hungarian phone directories today, nor is it found in the nobility literature.
Bánhidy is found in the Hungarian phone directories, and there are probably many more in Romania. But they seem to be quite scattered, most frequently in Eger and Szeged, and none in Csongrád.
I see you have posted on Radix with considerably more information, including a connection with Glogowatz, now in Romania. Have you looked at all the websites dealing with Glogowatz, including an offer to do look-ups? Have you also scoured all the possible church records for your place names?
Let me know if you would like any of the entries in the nobility literature on the Bánhidy family. It is mostly in Hungarian except for Siebmacher, which is in German.
Janet