Can a father have access if he is on the sexual offence record 2003 for having sex or numerous occasions with a child of the age of 13 and he was 19?

Yes of course, this does not show him a danger to his own child. The court may, if requested, have monitored visits at first ( but I doubt it) Sex offenders, are many things, most are no danger to small children and esp not to their own children.