Is it possible to change the value of system field in Jira cloud through REST API?
Welcome @TatjanaArangjelova to the Atlassian developer community.
Unless I misundertand your question, the simple answer is yes, using PUT /rest/api/3/issue/{issueIdOrKey} to edit an issue.
Where things get confusing is the concept of “system field”. In the examples, you can see fields like summary and components, which are obviously system fields because they have a name that you’ll find common in all Jira instances. However, many fields provided by default Jira project templates and available in JQL as names are actually custom fields in the REST API. So to set many common “system fields” you still have to search for a field by name to get an id. One way to do that is to GET /rest/api/3/field/search to get a paginated list of fields.