That would refer to the Militia. The High Sheriffs and later the Lord Lieutenants of the counties of England and Wales [later Scotland & Ireland]were empowered by Act of Parliament to raise a force of Militia for home defence. The ballot was an early form of conscription, the names of all suitable men were collected and then the “quota” was selected by ballot. Although intended for home defence, many men, tempted by a cash bounty, elected to serve in or along side regular army regiments abroad. The Militia Act was modified at various times and later it became a wholly volunteer force, but the “home defence” principal remained the same.
It was possible for the son’s of the more wealthy to get around the ballot if the were selected by “paying” another to be their substitute. It may be the phrase means that in his case he was forced to take up his own place by his father or it could be that he was simply selected to serve.
Some records of militia do survive at the National Archives, Kew in WO13 and WO68 and at some Country Archives [Record Offices].