What is the ruling on one from whom mathi (pre-seminal fluid) was discharged due to thinking before the Ifadah circumambulation, and is a fidyah (expiatory offering) obligatory upon him, and is he allowed to choose in the fidyah due to his inability to slaughter a sheep?

The emission of madhy (pre-seminal fluid) merely by thinking is not among the prohibitions of ihram (definition), nor among the nullifiers of Hajj. Your Hajj is valid, and you are not required to offer a fidyah (definition) (expiatory sacrifice) according to the majority of scholars. However, the Malikis hold that an offering is obligatory for whoever emits madhy, whether by thought or otherwise. It is necessary to ascertain whether the discharge is madhy or maniy (seminal fluid). Madhy is impure and invalidates wudu (ablution), and it necessitates washing whatever it soiled of clothes and body. As for maniy, it necessitates ghusl (definition) (ritual bath) from janabah (definition) (major ritual impurity).