Which branch of philosophy aims to determine the nature, basis, and extent of knowledge?

The answer is "Epistemology".

Epistemology examines the idea of information, defense, and the soundness of conviction. A great part of the open deliberation in epistemology focuses on four regions:

1) the philosophical investigation of the idea of information

2) various issues of distrust

3) the sources and extent of learning and supported conviction

4) the criteria for learning and support.