The question of how much influence a parent has in who their child becomes is studied by?

Developmental psychologists

Explanation:

Developmental psychology is defined as the scientific study that why and how a person change over their entire lifespan. It explains that how the thinking, behavior and feeling of a person changes throughout their life.

Parent have great influence on their child's mindset and there are several instances where parent's thinking determine what their child become in near future. For example, during toddler-hood babies learn to walk and talk and with time development of language take place which is largely determined by the behavior, thinking and feeling of parent.