Section 1. In Suffolk county the treasurer of Boston, and in Nantucket county the treasurer of the town of Nantucket, shall be the county treasurer. In all other counties, a treasurer, who shall be a resident of the county, shall be elected as provided in section one hundred and sixty of chapter fifty-four, for the term of six years beginning with the first Wednesday of January following his election and until his successor is qualified. No incumbent of the office of attorney general, district attorney, justice of the superior court, clerk of the courts or sheriff shall be county treasurer.