I want to find supernova candidates by using the Gaia catalog in 300 parsec (near Earth). I though they must be red super giants so they are cooler than 4100 K and more luminous than 104 solar luminosity. However, there is no data for luminosity for those stars. So I need another parameter related with brightness, magnitude or luminosity etc. Any suggestions?
If you are just interested in supergiants (note that the massive progenitors of supernovae are more likely to be main sequence stars, since that is where stars spend most of their [short] lives) then the problem amounts to selecting stars in a certain portion of the observational Hertzsprung-Russell diagram (absoloute magnitude versus colour). In the case of Gaia DR3 (or EDR3) this woud be absolute G magnitude versus Bp-Rp.
I do not know what restrictions you want to place on the types of progenitor you wish to find but let's say that you wanted stars cooler than some colour and with an absolute magnitude less than -5 (the absolute magnitude of Betelgeuse is about -6).
The distance modulus at 300 pc is $5\log d -5 = 7.38$, so your candidate stars would have to be brighter than about G=2.38 (if the star was closer than 300 pc, or more luminous, then of course it would be brighter). NB: I have however ignored extinction, but this should be a small effect within 300 pc.
So you go to the Gaia catalogue and request all stars brighter than G=2.38 and with a parallax greater than 3.333 milli-arcsec. From these few stars you can choose the ones in the colour/temperature range that you want.
Unfortunately you will probably find that data for extremely bright stars (G<3) is missing from the Gaia catalogue. The stars are too bright to be recorded and measured properly.
You probably would do better by search the Yale Bright Star Catalogue for objects with V<2.38 and a colour redder than some threshold (the catalogue also has spectral types, so you could just strip out the class I luminosity sources using this). You will then have to individually search for distance information to those stars (their parallaxes will not be very good).
You might find Messineo & Brown (2019) of interest. They produce a catalogue of red supergiants using the Gaia DR2 data (which still has the bright star problem).