Caesar Augustus was the first Emperor of the Roman Empire. He succeeded the dictator Julius Caesar and was succeeded by Caesar Tiberius. Some claim Tiberius was co-regent with Augustus for a couple years prior to Augustus' death, but this is disputed. A co-regency is the situation where a monarchical position (such as king, queen, emperor or empress), normally held by only a single person, is held by two or more.
This is an important issue to historians, as it affects the dating of the life of Jesus. Had there been a co-regency, Jesus could have started His ministry as early as AD 26 or 27, allowing for AD 30 to be the date of Jesus' death. Had there been no co-regency, His ministry would have started at about AD 29, putting His death around AD 33.
An article from the creationist web site Answers In Genesis says (see Conclusion)
[S]ome have postulated a co-regency (joint rule) of Tiberius and Augustus during the last few years of Augustus’s reign. However, there is no reliable ancient historical evidence for such co-regency.
Is there any historical evidence for Caesar Tiberius having a co-regency with his predecessor Caesar Augustus?