A Dorchester man pleaded guilty yesterday to gun charges after a fingerprint tied him to an incident last year, according to Suffolk District Attorney Daniel F. Conley. Jamaine Burton, 21, was identified as the gunman outside a party in Dorchester who ran from police on May 16, 2010, Conley’s office said. Burton and another man were later apprehended. A resident of Harvard Street found a handgun that had been thrown into his yard during the chase, and police found Burton’s fingerprints on the weapon, Conley’s office said. Burton was sentenced to three to five years in state prison on charges of unlawfully possessing a loaded firearm and two counts of assault with a dangerous weapon, according to the district attorney’s office.