What is the source for the commonly held belief that Minhag is inherited from the father, rather than the mother? Does this also apply that the wife inherits the husband’s minhag? Or she keeps her own?

ב"ה Shalom To put things in order, it should be said first that the mother is required to follow the customs of her husband. This is learned from the Mishna in Pesachim (Chapter 4) that one goes from one place to another, he adopts upon himself the customs of the new place. Similarly, when a woman marries her husband it is like she has left her previous place of custom and has arrived at a new place. Rav Moshe Feinstein zt"l in his sefer (אגרות משה או"ח ח"א סי' קנח) says this applies whether the custom is more stringent or lenient. It then follows that a child follows the custom of his parents which is essentially his father's. Following the custom of the fathers is discussed in the the Talmud in Pesachim 50b, and is mentioned in the Halachic literature over the generations. The Rashba views following the custom of the fathers as the transmission of the Torah from generation to generation. שו"ת הרשב"א ח"ג תיא)) Happy Chanuka