While imprisoned by House Stark, Ser Alton and Jaime Lannister talk about Willem Frey's wedding. Ser Alton mentioned he filled in as Jaime's squire, when Bryan threw up on his horse. Jaime said it was Tyrion who made him so drunk.
In the booksEdit
In the A Song of Ice and Fire novels, there is no mention of Jaime ever having a squire named Bryan.