Hi, welcome to BYC!
We have loads of mosquitos here as well, and the same basic scenario. My hubby saw a trap made by dynatrap at Costco (poor rated model). Different models have different prices and ratings as well. I haven't yet made the investment but I may before too long. I am still researching but a lot of them said it caught every insect EXCEPT mosquitos.
A fan does work pretty good for us when it isn't too cool. And I often get bitten when I am unsuspecting because of being in the sun.... Don't they know how to play by the rules?
I hope you get more suggestions. I am following along.
I have found, most of the plants they say repel mosquitos don't work well if they aren't fresh cut or smashed or something. For example I have seen them land directly on mint and cat nip like it was no big deal.
I have also made a trap using a 2 liter, top inverted with sugar water and active yeast (to make co2) but I think our weather was to cool for the yeast to work fast enough for the intended effect.
Another homemade trap is dry ice inside a plastic bag (the 2 liter might work better). As it melts, same thing co2.
I HATE MOSQUITOS WITH A PASSION!
Good luck.