The Proto-Chadic word for "go out" was reconstructed by Newman and Ma (1966) as *p-t-, with attested reflexes in all primary subgroups of the family; the best known of these is of course (West Chadic A.1) Hausa fìtā. The vowels vary across languages, and there is often no final vowel. Only one subgroup, as far as I can see on a quick check, shows the consistent vocalisation *patā: the Bole languages (West Chadic A.2), spoken in Nigeria's Yobe State along the boundary between Hausa and Kanuri. Thus Bole pàtā, Ngamo hàtâ, Karekare fàtā.
Most Songhay varieties have reflexes of two near-synonyms for "go out": *hùnú and *fáttá. Usually, the distinction seems to be roughly "leave (a place or event)" vs. "go out of (an enclosed or concealed space)". In Northern Songhay - the subgroup most isolated from the rest for longest, spoken in the Sahara - only reflexes of *hùnú seem to be attested, covering both senses (eg Korandje hnu). This could be interpreted as reflecting Northern Songhay's general tendency to reduce its inherited vocabulary by widening the usage of generic terms. In light of the Chadic data, however, it is tempting to interpret it the other way around: did Northern Songhay preserve the original situation, while a West Chadic borrowing spread throughout the rest of the family via the Niger River?