The laws of respect relevant when the son is his father’s Teacher and Rebbe in Torah learning:[1]

Who stands for whom:[2] In the event that one’s father is a student of his son in his Torah learning[3], then each one is to stand on behalf of the other. [The son is to stand on behalf of his father in order to honor his father, and the father is to stand on behalf of his son in order to honor his teacher and Rebbe. However, there are Poskim[4] who argue on the above and rule that a father is to never stand on behalf of the son even if his son is his teacher and Rebbe. Practically, one is to suspect for this opinion and therefore the son should forgive his father and not require him to stand for him.[5] If, however, the son is a famous Rabbi and his father is not well known in the city then they are to keep a distance in order so the son not need to stand for his father as this may appear like a belittlement of the Torah, as explained next.[6]]

May the son serve his father:[7] In the event that one’s father is a student of his son in his Torah learning, then the father may not have his son serve him, although if the son chooses to forgive his honor and serve his father, then he may choose to do so, as a Rebbe who forgives his honor, his honor is forgiven. However, this ability for the son to forgive his honor and service his father applies only in private, where no one will see him do the service. Alternatively, it is also permitted to be done in public in a city where everyone knows the father and son relationship and know that the individual that the Rabbi is serving is his father. If, however, the son is a famous Rabbi [i.e., Gadol Batorah] and his father is not well known in the city, then he may not forgive his honor and serve his father, as this may appear like a belittlement of the Torah if the son belittles himself before his father. Accordingly, in such a situation, the father and son are to keep a distance [while  going out in public in the city] in order so neither one is lenient in the honor and respect of his fellow. This was practically followed and done by the Maharam when he was together with his father [in a certain city in which the father was not well known but the Maharam was]. [In fact, they write of him, the Maharam, that from the day that he became a Torah leader, he did not go to greet his father, and he did not want his father to come to greet him.[8] Other Poskim[9], however, rule that it is not proper for the son to distance himself from his father, and rather he should forgive his honor and visit his father. According to all Poskim, there is no need to move cities if he lives in the same vicinity as one’s father.[10]]

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[1] Michaber and Rama 240:7; See Encyclopedia Talmudit Erech Kibud Av Vaeim Vol. 26 p. 450-453

Father versus Rebbe: Regarding what is to receive precedence, assisting a father or assisting one’s Rebbe, see Encyclopedia Talmudit Erech Kibud Av Vaeim Vol. 26 p. 447-449

[2] Michaber 240:7; Tur 240; Rosh Kiddushin 1:57; Rameh, Riaz and Piskei Rid Kiddushin ibid; Pesakim Uteshuvos 240:28; See Likkutei Sichos 5:310; See Encyclopedia Talmudit Erech Kibud Av Vaeim Vol. 26 p. 427 footnote 749 that Rebbe Yehoshua Ben Levi stood up for his son; Poskim in Encyclopedia Talmudit footnote 1055-1056; See Kiddushin 33b that the Talmud leaves this matter in question, and these Rishonim hold that we must be stringent on both sides; See Encyclopedia Talmudit ibid p. 450 footnotes 1034-1068

[3] Regarding if this applies only if the son is his main Torah teacher [i.e., Rabo Hamuvhak] or even if he simply is one of his teachers, see: Amudei Arazim on Yireim 56:6; Chazon Ish Y.D. 149:5

[4] Shach 240:10; Rambam Mamrim 6:4; Rabbeinu Chananel; Teshuvos Harameh 71; Radbaz Mamarim 6:4; Rishon Letziyon 240:7; Chaim Sheol 2:43; Mitzpeh Aryeh 8; Poskim in Encyclopedia Talmudit ibid p. 451 footnote 1049-1054; See Kiddushin 33b that the Talmud leaves this matter in question, and these Rishonim hold that practically we conclude that only the son must stand

[5] Rashal Kiddushin 1:72; Sefas Emes 240

[6] The Maharam was stringent in this matter that from the day that he became a Torah leader, he did not go to greet his father, and he did not want his father to come to greet him in order so they do not enter the question of who is to stand on behalf of whom. [Taz 240:9; Rosh Kiddushin 1:57; Rabbeinu Yerucham Nesiv 1:4; Radbaz 8:165; See Encyclopedia Talmudit ibid p. 452 footnotes 1057-1058]

[7] Rama 240:7; Bach 240; Perisha 240:13; See Hagahos Rebbe Akiva Eiger 240:7; Tosefes Kesuba  on Kesubos 103; Haflah Kesubos 103a; Pesakim Uteshuvos 240:28; Encyclopedia Talmudit ibid p. 452 footnotes 1059-1068

[8] Taz 240:9; Rosh Kiddushin 1:57; Rabbeinu Yerucham Nesiv 1:4; Radbaz 8:165; See Encyclopedia Talmudit ibid p. 452 footnotes 1057-1058

[9] Radbaz 8:165; See Birkeiy Yosef 240:2; Yifei Laleiv 3:20; Aruch Hashulchan 240:26

[10] Rashal Kiddushin 1:72