Yes, T310c AP is supported on SZ144 running 6.1.2.
By default the AP will join the 'Default' AP zone. If the default AP zone is running 6.1.2 version T310c should be able to join.
Please refer page 8 of the release notes for 6.1.2 to see the list of all AP models supported.
https://support.ruckuswireless.com/documents/4633-smartzone-6-1-2-lt-gd-release-notes
