Which Antenna for VHF/UHF ?

What do you think of use Microstrip Patch Antenna for 240-320 MHz? I knew it's rarely designed for this bandwidth.

Yes, and there is a reason why. Path antenna is narrowband by design.

Which antenna can be designed for this bandwidth alternatively to Patch Antenna?

For wideband VHF/UHF, have a look at log periodic antenna.

Google will also show you examples how log periodic is implemented on PCB, but obviously it will be large for this frequency range.

The bandwidth is not too wide so log-periodic antenna is not necessary imo.
Omni-directional Spiral Antennas are widely used in near to this band for military/avionic short range ground-field communications.
But i don't know exactly what your intention is..

I'm not sure about your application but Vivaldi Antenna may be a good starting spot for you.

As P.Gibson mentioned on his Vivaldi Aerial patent, this type of antenna has good performances in 2GHz-40GHz frequency range.
In a Vivaldi antenna, the slotline to free space transition is given by exponentially flared slotline.
In order to get efficient radiation in free space, the width of the open end should be greater than λo/2.
At 240MHz this dimension should be greater than 62cm, which makes the overall dimensions of the antenna to be great.

At these frequencies, patch antenna with air dielectric has the same great dimensions issues.
Increasing the dielectric constant of the substrate reduce the dimensions of the patch antenna, but the antenna still have narrow bandwidth.

A patch would not be my first thought for this frequency range. I concur with the bandwidth comments above. Bandwidth could be increased significantly with a stacked design and air dielectric but the antenna would be physically large. Stacked patches can get into the range of 50% bandwidth but it is not trivial to achieve. I did it once with two parasitic plates at a much higher frequency, 2 GHz or so as I recall. s11 bandwidth was around 50% and the patterns were not too bad over the same range. The gain was around 4 to 6 dBi. A big ground plane would be helpful if you can find room.

How about something like a sleeve dipole or bow tie? It might be easier.

Regards,

Azulykit