Your paternal Irish ancestors are Scandinavian. Haplogroup I2b1a is a common indicator of Anglo-Saxon or Viking"invaders" into the British Isles. Native Irish haplogroups are invariably some variety of R1b. I've many male cousins who are R1b1b2a1a2f*, both Irish and Scottish in origin.
Here is what the ISOGG has to say about the I Y-DNA Haplogroup, quoted verbatim.
"Y-DNA haplogroup I is a European haplogroup, representing nearly one-fifth of the population. It is almost non-existent outside of Europe, suggesting that it arose in Europe. Estimates of the age of haplogroup I suggest that it arose prior to the last Glacial Maximum."
"The two main subgroups of haplogroup I likely divided approximately 28,000 years ago:"
"I1-M253 et al has highest frequency in Scandinavia, Iceland, and northwest Europe. In Britain, haplogroup I1-M253 et al is often used as a marker for "invaders," Viking or Anglo-Saxon. The I1b-M227 subclade is concentrated in eastern Europe and the Balkans and appears to have arisen in the last one thousand to five thousand years. It has been reported in Germany, Czech Republic, Poland, Estonia, Ukraine, Switzerland, Slovenia, Bosnia, Macedonia, Croatia, and Lebanon."
"I2-M438 et al includes I2* which shows some membership from Armenia, Georgia and Turkey; I2a-P37.2, which is the most common form in the Balkans and Sardinia; I2a2-M26 is especially prevalent in Sardinia. I2b-M436 et al reaches its highest frequency along the northwest coast of continental Europe. I2b1-M223 et al occurs in Britain and northwest continental Europe. I2b1a-M284 occurs almost exclusively in Britain, so it apparently originated there and has probably been present for thousands of years."