A user has permission to edit a field via a Permission Set but is unable to do so.
Permission Sets cannot provide edit access to a field which has been designated as read only on the page layout. This article provides information on how to turn off the page layout permissions. Review the help information on What Determines Field Access for more information.
The only permission which grants the ability to edit fields that are set to read only at the page layout level, is the Edit Read Only Fields System Permission which is global in nature (Applies to all Read Only Fields in the System).
Summary: Permissions sets can override field-level security, however, they cannot override page-layout security.
The following steps will remove the Read Only designation at the page layout level.
When using Salesforce Classic:
For Standard Objects
For Custom Objects
When using Lightning Experience
Verify Access for a Particular Field
Some Users can edit fields set as 'Read-Only' in field level security and page layout
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