Barton has been found guilty of gross misconduct following the offence on Friday 22 July. He has been fined a total of eight weeks wages, including two weeks carried over from a suspended fine following a previous disciplinary hearing in December last year.
The midfielder has also agreed to undertake a programme of rehabilitation in a bid to prevent incidents of this kind occurring again.
Club spokesman Paul Tyrrell said, ‘Joey has expressed his deep and sincere remorse over the incident and is keen to make amends to this football club and our fans who expect the highest standard of behaviour from our players.
‘He has apologised to those involved and has accepted his fine unquestioningly.’
Barton added, ‘I understand the distress I have caused to everybody concerned and want to apologise for my actions.
‘I am grateful for the support I have received from the club and my friends and family.’