Quick dive in to answer a question:
Patristics is an era in the history of the church, generally from the end of the Apostolic era (c100AD) to, I would say, the first millennium.
Generally it's the study of the Church Fathers (hence the name) – the theological heavy hitters of the early church. Generally the sources are split to before or after the Council of Nicaea (325). Also, the distinction between Latin and Greek. I favour the Greek. My pin-ups are Irenaeus of Lyon, Athanasius of Alexandria and Maximus the Confessor. And Origen. Of the Latins, I suppose Tertullian, Ambrose of Milan, Augustine of Hippo.
BTW, the Letter to the Hebrews is generally dated early to mid 60s. Paul's execution is supposed around 64. Right from the get-go there were Fathers said Paul was unlikely to be the author, but when I was a kid it was in the Sunday Missal as 'St Paul's Letter to the Hebrews'.