First you consider whether he/she is guilty of the crime for which they were convicted – or any other crime associated with the case.
If the convict was at the scene, took any part in the action, was associated with the action in any way you will not succeed in getting him/her out of jail. What’s more, you will spend so much time and money trying to prove a case of innocence that there will probably be severe family splits about the matter. Some members of the family will want to get on with their own lives and resent the fact that the convict got him or herself into trouble. You may continue, spending time and money that could better be spent elsewhere - and cause a family split.
Beware this – the person may well come out of jail in such circumstance with no one to help him get back into society – because the attempts to get him out of jail have caused so much stress and agony within the family.
This is a very serious point – because if the convicted person is in any way guilty you are very unlikely to succeed in winning an appeal. And there are other priorities.
If the person inside already has form for previous crimes, there is very little chance of getting an appeal. This is nothing to do with the authorities involved. It is just the way of the world. The general public take a dim view of people who have done crimes - and they are not willing to help anybody like that. So once tarred, you are tarred for life. And anyone investigating a supposed miscarriage of justice will need the help of members of the public , so its going to be very very hard to get them to help. .