A parti-yorkie is an akc registered yorkie that cannot be shown in the ring.
A Biewer is a rare breed dog. Registered either in the U.S. or Germany. Come look at the Biewer Breed Club of America for complete information:
Biewer Breed Club of America Inc. BBCA
Also do a search here on YT as there has been a lot of discussion about Biewers and Partis.