Which parenting style is demanding and controlling, while also being rejecting and unresponsive?

The answer is the authoritarian parenting style.

There are 4 known parenting styles, these are as follows:
(1) Neglectful
(2) Indulgent
(3) Authoritarian
(4) Authoritative

Each one of the parenting style have different characteristics.

In the neglectful parenting style, the parents are undemanding, not controlling, rejecting, and unresponsive. The parents do not have care for the child.

In the indulgent parenting style, the parents are undemanding, not controlling, generally accepting whatever their child's behavior, and responsive. These poses the risk of the child being a spoiled brat. 

In the authoritarian parenting style, the parents are demanding and controlling, while also being rejective and unresponsive. This kind of parenting style are the so-called super strict parents. 

Lastly, the authoritative parenting style, the parents are demanding and controlling while being acceptive and responsive. This offers balance between the child's invoice and the parents' authority.