‘Widuję’ is derived from ‘widywać’. This is the frequentative from of ‘widzieć’. (A frequentative form indicates a repeated action).
Good idea to share this with other learners!
Frequentative forms carry the meaning of “from time to time”. There are very few of them in Polish—something between 6 and 10, I think.
Some other frequentative verbs (roughly from the most common to the least commonly used):
- bywać (“to be”)
- jadać (“to eat”)
- czytywać (“to read”)
- pisywać (“to write”)
- chadzać (“to walk” / “to go”)
I thought, that as this is such a rare form of verb, I would leave a note for myself and for other learners.