Is there any preprocess hook for date api?
Date API introduces several theme functions:


theme_date_combo
theme_date_display_combination
theme_date_display_interval
theme_date_display_range
theme_date_display_single
theme_date_text_parts


All of which can be preprocessed.

If the output you need to override isn't the result of one of those functions, you'll need to look for a different solution (e.g. depending on context you might be able to preprocess a field template).