I'm a USA citizen. My fiancé is in jail in another country. Would he have a problem of coming here after i file for his green card?

It will depend upon the exact charges for which your fiancé was convicted and the sentence imposed. Your fiancé may be required to show additional equities to or seek a waiver to secure a visa. Your fiancé could be ineligible for a visa. I would encourage you to obtain copies of his criminal record and have it reviewed by an experienced immigration attorney. You can read more about the family immigration process at http://myattorneyusa.com/family-immigration.