Tiberius was the adopted son of Augustus and of the life of the Claudii. He was a successful general and a decent politician. His lineage was impressive though. However, there was no god in the Roman pantheon called Tiberius. I think what you might mean is that Tiberius was deified. In this sense, he was a "god," but I would assume that most people did not consider him a god. After Caesar, the emperors had a "divine status," which people like Tiberius enjoyed, but again it is hard to say what people actually thought of this whole process. For example, Seneca wrote a play mocking this very notion, the pumkinification of Claudius. If you want to read about Tiberius, read the works of Tacitus and Suetonius' biography on Tiberius. These authors have a very negative picture of Tiberius. You will find many details concerning him.
What is known of Tiberius Julius Ceasar Augustus is that he was not a God. There is no god Tiberius in Roman mythology. However, there is was a very powerful emperor that, just as his nephew Caligula, declared himself one and almighty.
Tiberius Ceasar (AD 14-37) was one of the worst emperors in the history of Rome. He was a syphillitic, sexually perverted abuser who did his best at doing the worse during his reign.
He set off wars for no reason, and he would keep a harem of children for his disposition. He adopted Germanicus, who was a fantastic soldier who died way too early in life. It was Germanicus son, known as Little Boots (Caligula) who would precede Nero, and eventually the entire bout of Tiberius, altogether, formed the Reign of Terror in Rome until the day it burned.
First of all, you should know that he is not one of the gods in the same sense that Jupiter and Mars and Pluto are gods. The official Roman religion held that every emperor became a god (but not a major god like the ones I mentioned) after he died.
Tiberius was emperor of Rome from 14 AD until he died in 37 AD. This means that he was the emperor of Rome during the time that Jesus is said to have been crucified by the Romans in Jerusalem. He was the adopted son of Augustus Caesar and that is how he came to be emperor.