Yes, you can attach files to issues with the REST functions. You'll just need to code a simple REST connection into your web-service and work out some way for the web service to know which issues to attach the files to.
https://docs.atlassian.com/jira/REST/latest/and https://confluence.atlassian.com/display/DOCSPRINT/The+Simplest+Possible+JIRA+REST+Examples are the places I start with REST.
It's not really a field though, it's just "attachments"
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