To Fast What We Owe

Miscellaneous Issues Regarding Intention
To Fast What We Owe
I fasted one month or so intending qaḍā’ fast if any; otherwise to be considered for the proximity to Allah in general. Is it considered as qaḍā’ of my missed fasts?
A: If you intended what you were required at the time fasting, whether qaḍā’ or mustaḥabb, and performed fast while you owed some qaḍā’ fasts, it is considered as qaḍā’ fast
Source: Hadana adopted from the Istiftaat of the Grand Ayatollah Khamenei