Assuming run the followed filter:
project = DEV AND status = "In Progress"
Usually, JIRA display the results on GUI.
However, instead of display results, I'd like to save them localy as file on JIRA server.
Alternativly, save this on a remote folder.
What is the best practice to do so?
your question could also be understood in a way you want to do something programmatically for issues, but "outside" of Jira - not really "outside" by means of "without" but just not having a user to interact with UI.
Therefore REST API access comes to mind, please find some examples here:
Output can be easily saved into a file - the specific implementation will depend on which programming language you will be using for REST API access. In the examples from Atlassian you will see just 'curl' which is a pretty simple command on common linux distributions (you invoke curl from shell).
Some people however prefer accessing REST API using another language, PHP, Python, C# - there are plenty of options. Very easy is the approach using 'curl'.
In case this was not understood correctly you're happily invited to explain a bit more on the use case ;)
There's a bit of a language issue here, with Jira-speak trying to be quite specific with certain words within the Jira context.
Broadly, when I hear people use certain words, I take them to have specific Jira meanings:
Search: a question you ask of Jira to get it to give you a list of matching issues. ("Show me issues where field X = Y" for example)
Query: same as "search", but usually more technical, in that I would expect it to be the actual definition (you could take a "query" and paste it into a search box and it would give you a list of issues!)
Filter: A query that has been saved in Jira, so that we can use it again. The results might change, but the question being answered is the same - "what issues match this question at the moment?"
Search/Query/Filter results: a list of issues that match the question
Note that none of those lead to anything more than "a list of issues" - they have nothing to say about what you do with the list of issues, the data from them that you show, how they might change, etc.
So, when you say "save filter", I am not quite sure what you mean. Can you confirm that you want is "ask a question at this point in time and 'save' the list of issues (and maybe some/all of the data on them) somewhere"?