How to speed up the local clock synchronisation?

I am running a ntp server, using the following configuration :

server 127.127.1.0 minpoll 5 maxpoll 5 iburst burst
fudge 127.127.1.0 stratum 0 refid GPS

Is there a way for my server to select this local clock faster than the default 5 minutes ? Minpoll and maxpoll increase the reach faster but it is not used in the clock selection.

Delete 127.127.1 lines. Undisciplined local clock should not be used. Certainly not misleadingly set to refid GPS. (If you have some other non-ntpd way this system's clock is disciplined, please explain.) As a driver "of last resort", it disables itself if another is in use. A normal state, you don't want LOCAL, as most general purpose computer clocks are not that accurate.

If you have locally attached stratum 0 hardware, add server lines with actual drivers. For GPS, NMEA for standard protocol. SHM for shared memory to another program like gpsd. Add PPS if hardware supports it. Ask the vendor for how to use it and example configurations.

Also add NTP sources, that you maintain or from the internet. More is better, allows detection of false tickers as a sanity check.

pool 2.pool.ntp.org iburst

Consider ntpd -g option to allow the first adjustment to be a step of unlimited size.

Restart ntpd on the new configuration. Monitor how it performs with ntpq -p