Some of the shuyookh of yemen and also a group of the scholars say if there is a difference of opinion on when the month began, one can fast a day before and after the assumed day of Aashurah.
Ash-Shaykh Muhammad bin Saalih al-Uthaymeen, rahimahullah, said:
إذا شك الإنسان في دخول الشهر فلا حرج أن يصوم ثلاثة أيام
If the person is doubtful pertaining to when the month entered then there is no harm for him to fast three days.
AbdulFattaah bin Uthman