I have found a James Fox Service #2207 in the 24th Regiment. He was born in 1825 in Armagh, Ireland and enlisted on 1 Apr 1842 aged 17. If you think this is your man, his Chelsea Pension Discharge Papers are online at findmypast.com but you will need to access a subscription to the website.
He was discharged at his own request after serving over 21 years in the Army. There is no mention of service in the Crimea, but he did spend nearly 15 years in India and was awarded a medal and two clasps for serving in the Punjaub Campaign 1848/49.