Does a father's preventing his daughter from completing her university education—without a clear reason, and at a non-mixed university, and with affordable costs—count as injustice towards her, and what is the way to convince him of that?

It is the father's duty to spend on his child and teach him what he needs. Therefore, his failure to encourage his son to complete university education, and his refusal, even though the son does not need his financial support, is considered an injustice. This is because a father is not permitted to prevent his son from seeking knowledge if the son's maturity, righteousness in religion, and intellect are established, even if the prevention stems from mere foolishness.

To resolve the issue, it is advised to discuss the matter with the father, and seek the help of righteous people and relatives to persuade him, while continuing to honor and be kind to him, and supplicate to Allah Almighty.

If the father is not convinced, one can resort to studying through an external enrollment system or distance learning. If all of that is impossible, then this is not the end of the road, for the bounty of Allah is vast.