I suspect it means 'Assaulting Habitation'.
At the Ennis Assizes in 1835, Thomas Brassil, with accomplices Edward (a.k.a. Ned) Neale and Patrick Loughnane, were sentenced to be transported for life for an armed assault on the house of James Gloster Esq., Ballykinnane.
A report of the incident in the Clare Journal and Ennis Advertiser of 9 March 1835 started : 'Thomas Brassil was indicted for assaulting the habitation of James Gloster at Ballykinnane, on the 4th of May, and also with firing a gun with intent to kill and murder him.' The report also mentioned that Neale was related to Brassil (it didn't say how).