Not really. It originated in SW Ethiopia and spread out encompassing most of Somalia. There's a reason why we're thought to be offshoots of Oromos. They're the first inhabitants there and we got Waaq from them too.
Around 80% of Smalis have it but around 80% of Ethiopians have it too. We might have the higher frequency by a few %-iles but there's no difference. Take into consideration Ethiopia has entire regions dedicated to Nilotes and Omotes such as the Benin Shangul region in the West (taken from expansion) that's why it says 40% to 80% here----->
View attachment 81071
That map seems to be wrong. This one shows that northern Somalia and southern Eritrea have more significant amounts of the J haplogorup
The Tigrayans and Amharas being descended from Semites isn't part of their oral tradition at all apart from the Solomonic dynasty which only refers to a single direct lineage of a single family, but even that refers to the biblical Solomon who married the Cushitic queen known as Sheba. Apart from the royal family and a couple insignificant villages/tribes in Ethio/Eri there's nothing else. They don't claim Arab lineage even half as much as Somalis have since we even existed. The location shown by the map I posted seems to show nearly 0% admixture with the J-haplogroup in Ethiopia lol apart from southern Eritrea and northern Somalia.
I highly doubt there's any signifiant amount of paternal Somali DNA in the Arab Peninsula, the opposite seems to be the case.