All Afro-Asiatic speaking groups share common ancestry (Egyptians, Semites, Cushites, Omotics, Berbers). There is no special link between Berbers and Cushites beyond the ancient Afro-Asiatic ancestry all share going back to about ~10,000 to ~8,000 BCE.
The major 'out group' are Chadics. Who have very little autosomal Afro-Asiatic ancestry. They are almost completely of Niger-Congo origin with minimal Nilo-Saharan and Afro-Asiatic input, nevertheless they carry R1b-V88 from the Middle East on their paternal side due to a founder effect that is not representative of most of their ancestry.
Cushites are also not completely 'Afro-Asiatic' ancestry-wise, a large portion (40% to 60%) of their ancestry derives from Nilo-Saharan groups similar to the Kunama and Nara who probably mixed with the Cushites as they migrated into East Africa from Egypt. The Nubians of North Sudan retained their Nilo-Saharan language and never adopted an Afro-Asiatic language, yet they are autosomally very similar to Cushites and closer to Cushites than the Berbers, Semites, and Egyptians are.