Every User can create & save its own issue searches and boards
issue searches and jql
If you want to just create a filter to return a list of issues - kind of like an ad hoc report - then you can follow what Alexander points to above.
However, if you want to change the filter on the board itself or how the board operate, you will need to be a Board Administrator or a Project Administrator for that project/board.
In addition to the guide for Advanced Searching linked by Alexander, you can save that query as a Saved Filter (as in a predefined search) using this guide: https://support.atlassian.com/jira-core-cloud/docs/save-your-search-as-a-filter/
If you mean "filter the backlog" as in add a Quick Filter, you'll need the board admin to create it, as described here: https://support.atlassian.com/jira-software-cloud/docs/configure-quick-filters/
If your use case would be advantageous for other users of the board, you could test your query in JQL, then ask the board admin to add it as a Quick Filter. Then you and all other users can utilize it to filter the backlog, in your board.
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