Love for a parent (father)

The love for one's children is parental. For siblings -- sisterly or brotherly.

How would one refer to the feelings towards one's parents, particularly -- the father?

Love for one's parents is filial.

Storge - familial love - denotes instinctual affection, such as the love of a parent towards offspring and vice versa.

Xiao 孝 (filial piety) "consists of reverent, sincere, self-sacrificing, and unconditional care for one’s parents while they are alive and after their death. [It] is one of the basic values of Chinese traditional culture in general and the basis for the development of the moral person in Confucian ethics in particular." - L. POŠKAITĖ (Asian Studies II (XVIII), 1 (2014), p.99)

I don't know of a word specifically denoting 'towards one's father'.