Patricia was part of a six song demo recorded at school friend Brian Roberts' home studio in Chiswick, London, that also included That's Me, Try a Little Sadness, Listen on Five, Don't Want You Back (aka Don't Wash Your Back) and She's Beautiful. Patricia was later re-worked as In Hiding while She's Beautiful morphed into The Serpent. This was the infamous tape that they got their friend John Alexander to leave in Jonathan King's car when he was visiting Charterhouse as they were too nervous to hand it to him in person. I would be very surprised if anyone could actually remember which of these was recorded first though.
Strictly speaking it wasn't really a Genesis session though, the band didn't exist at that point, they were just four songwriters trying to get someone interested in covering their songs. It was organised by Ant as a way of he and Mike getting some of their material down on tape. Ant asked Tony to come along and play some organ on it and he brought Peter with him and they talked Ant and Mike into recording one of their songs (She's Beautiful) with Peter singing - Ant was originally down to do all the singing. In the end it was agreed Peter had the better voice and he ended up doing all the vocals.