Is fasting intermittent days after interrupting a vow to fast two consecutive months due to illness, then breaking the fast out of negligence, considered a continuation of the vow, or must the vow be resumed with expiation? And what is the expiation in this case?

If you vowed to fast for two consecutive months, you must fulfill this vow, as the Prophet, peace and blessings be upon him, said: "Whoever vows to obey Allah, let him obey Him." If you break your fast due to illness, the continuity is not broken, according to the soundest opinion. However, if you break your fast out of negligence after your recovery, then the continuity is broken, and you must restart fasting the two months from the beginning as long as you are able to fast.