Embattled actor Timothy Busfield surrendered to New Mexico authorities Tuesday after a warrant was issued for his arrest in connection with child sex abuse charges — and insisted he was innocent and the disturbing allegations were “all lies.” The “West Wing” star turned himself in to the Albuquerque Police Department after cops alleged he engaged in unlawful sexual conduct with 11-year-old twin boys while directing the Fox show “The Cleaning Lady” in 2024, the police department confirmed to The Post.