76b says Rav Ada bar Ahava acquired a position of srarah for his guest because the guests's father was a ger, but his mother was a yisraelis.
Sanhedrin 36b brings a gzeiras hakasuv to allow a ger to be a dayan. However, Yevamos 102a says a ger may judge his fellow ger midioraissa and learns it from a pasuk. How can one gemara say a ger may judge everyone and another gemara says a ger may only judge his fellow ger? Rashi says that the Gemara in Yevamos is referring to capital cases; a ger may not judge a yisrael who's not a ger in a capital case. But a ger may judge everyone in dinei mamonos. If his mother was a yisraelis, he may judge everything, as our gemara here in kiddushin says - if imo miyisrael he can have srara positions. Rabbeinu David (Ran Sanhedrin 36b) asks on Rashi, that a 23-member beis din (which may judge capital cases) must be meyuchas. But a ger isn't meyuchas, so how can Rashi say a ger can judge a fellow ger in a capital case, if a ger may not sit on such a beis din? The Ran suggests that to Rashi there may be a 23 member beis din consisting of all geirim and they can only judge capital cases against geirim. Rabeinu David, however, answered when the gemara in Yevamos 102 said "a ger may judge his fellow ger" it means he may be appointed to a regular dayan in dinei mamonos for geirim, but when the gemara (Sanhedrin) implies a ger may judge regular yisraelim in dinei mamonos it means occasionally, but a ger may not have that as his permanent position, but if his mother was a regular yisaelis he may have such a position/appointment. Tosfos Yevamos 45b s.v. Keivan says that even if a yisrael married a giores, their son may be appointed; the child with aviv miyisrael has the same din as the son of a ger and a yisraelis, imo miyisrael.
Tosfos Yeshanim Yevamos ibid. say (to answer our original question - Daf 102 implies a ger can judge a Yisrael in dinei mamonos [like Rashi] but on 45b implies he must have imo miyisrael?) that even for dinei mamonos, a ger may only judge his fellow ger.
Rabbeinu Tam holds (Tosfos on gilyon, Yevamos 45b) that a ger may judge fellow geirim even with kefiya (force) but a ger may not judge a yisrael with kefiya. This is the psak of the Shach & Sma in C"M 7.
There is a daas yachid, Haghos Mordechai in Yevamos that a ger may not even judge his fellow ger with kefiya.