A kohen is a patrilineal descendant of Aharon HaKohen and must also be “kosher” from his matrilineal ancestry – meaning that his mother, grandmother, great-grandmother etc. where all rabinically fit to marry a their kohen spouses.
In the absence of kohen meyuchas certification, modern kohanim fall into two general categories – religious from birth and baalei teshuvah.
A kohen of the former sort has the status of kohen muchzak – this is so even in the absence of a lineage document.
What is the bottom line answer of who is a kosher kohen? its simple; the kohen who is recognized as such by his kehillah kedosha is deemed a kohen muchzak -a “status-quo” kohen. this is no small title as it carries with it numerous restrictions, responsibilities, and even privileges.
The kohen muchzak is considered a full and kosher kohen מן התורה (Min HaTorah -biblically).
Working in favor of the authenticity of todays kohen is the value of the term kohen muchzak; the entire concept of chazakah in halacha is founded on the base of the kohen being what he and others think he is -an authentic and kosher descendant of Ahron HaKohen. But again, this is just scratching the surface of a number halachic angles (such as all family’s have the chazaka of being kosher, an absence of A valid disproof of the kohen’s sound chazakah) that place the kohen muchzak as a fully authentic, kosher kohen.
The sdei chemed
The sdei chemed, a noted posek is one of many poskim who composed responsa to the issue of kohanim muchzakim -kohanim who are “status-quo” in their kehuna. He is one of the few though who did a thorough work of collecting, analyzing and deciding between those opinions discussed during and prior to his era; The sedei chemed on the kohen muchzak.
Kohen baal teshuva
The kohen baal teshuva often knows for certain that he is of patrilineal descent from a kohen, yet may be unsure of the kashrut status of his matrilineal line. Although we present a general overview of the halachic parameters involved, the halachic status of the said kohen is to be determined on a case-by-case basis by a local orthodox rabbi.