Currently custom field created using app rest api  can only be set using their ID and not value. 

Working Example:

 {
 "fields": 
{ 
"customfield_xxxx": <id>
}
} 

Non-working Example:

  { 
"fields": 
{ "customfield_xxxx": "<value>"
 }
 } 

It will be helpful if app custom fields can also be edited using their values.