Is there any transistor I can order which could work at 20V Vds with low threadhold voltage Vgs less than 1.5V, and it has around 300mA output current? Thanks.
If I wanted to know this, I´d use the interactive selction guides of manufacturers or distributors.
You can do the same on your own. The benefit is that you see additional informations like availabilitiy, price, package, r_ds_on ...
Almost any distributor and every manufacturer will give you this informations for free.
The threshold voltage of a Mosfet is the Vgs voltage that barely turns it on with it conducting only 0.25mA. An IRL540 has a maximum Vds of 100V and a Vgs(th) of 1V to 2V. Some of them need a Vgs of maybe 3V to conduct 300mA and need a Vgs of 4V to conduct 14A. There are some tiny Mosfets that conduct 300mA when Vgs is 1.5V but I don't know their part numbers.
You did not mention a need for a very low gate current then any bipolar 300mA transistor will work. Its base voltage will be about 0.7V.