The 'Familysearch' website shows a number of Higgins civil birth records registered in Oughterard district in the 1920s, including a Patrick in January 1926 and April 1927, and a Michael in July 1923, but I don't know if these were the children of John and Anne. Same website shows a Higgins birth in October 1928 registered in that district with the mother's maiden name given as Burke, (I'm withholding the forename in case alive, but you can see it yourself on the website), but again, in the absence of seeing the actual record, it's not conclusive.
Under the 100 year rule I'm not aware of any official source where you will find the content of these birth records shown online.