I have a select list having 2 options, security, network, and project roles security_role and Network_role,
When the ticket is in open status, and select list value is network then only users in network_role can edit the ticket, similar for security as well,
Kindly provide me some suggestion on this how I can achieve?
You can't do this on the value of a custom field. You can restrict edit by status though - see https://confluence.atlassian.com/display/JIRA/Workflow+properties
Nic is correct, this is not possible based on a field. Instead of using a select list use two issue types ("Secutity Issue", "Network Issue"). If you have for each issue type an own workflow, you can use those workflow properties to achieve your goal.
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