The correct answer to this open question is the following.
Although there are no options attached we can say the following.
Who had overwhelming support from the Legislative branch during the 1946 Governors controversy and later became the undisputed Governor after a special election was held?
Answer:
Herman Talmadge, the son of the elected governor Eugene Talmadge.
The controversy was created because Eugene Talmadge had won the election for governor of the state of Georgia in 1946, but he d¿suddenly died.
The legislation of the State of Georgia had not contemplated that situation and three people tried to be the new governor: Herman Talmadge(Eugene's son), Ellis Arnall(the former governor), and Melvin Thompson(the lieutenant-governor elect).
The Supreme Court of Georgia had to intervene and decided that Thompson would be the governor until further elections. In the elections of 1950, Talmadge won the election a became the governor of Georgia.