She has been a sore spot for me, as trying to trade with her seems like the a wasted effort since she has no mana and can spam out point and click abilities, with no real draw back. Her wave clear seems pretty strong as well, so how would you go about winning against her? Assuming you don't get ganked, it's just one on one.
She does not really have escapes aside from her flash. You need to camp her early and shut her down. If you are mid, take exhaust.
Harass her with poke. Let her have it whenever she's trying to last hit a cannon. Make it dangerous for her to go in on you. Zed, for example, destroys her with superior poke even before he becomes able to negate her ult by ulting her back.
I was going to give an Orianna example but I did not. I looked you up and you actually played Orianna. Definitely go exhaust against Kat, Zed, and Yasou. It will help you a lot more than barrier in that case.
You are a control mage. You can poke her down from a far using your q. You need to watch your minions health and hers. She go to CS a minion, you Q her until she no longer can lane against you. You can dictate where she goes by using smart q placement in lane effectively zoning her.
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Kat's dagger placement is her weakspot... she will no doubt try to jump to her dagger if you are near it, so play around it..If you can fake her out to jumping on her dagger try to CC her when she jumps to it. CC and mobility is a strong counterplay against kat, zed is a perfect counter to her. He can build maw and mercs, and R/W away from her ult while comboing her... But if you arent Zed..Just play around her dagger in a strategic manner, making her wish she hadn't jumped onto it. Save an knockups/escapes you have for when she ults :)
You deal with katarina in three ways
Option B: Take the AFK push champions so you wont ever have to interact with her, and she cant roam. (Make sure to ward behind the bush so you can easily ping if shes coming bot side or not)
Option C: You picked a matchup you are likely to die in or it's a skill matchup but you don't have confidence in the lane. Just take 
and make sure to ward her roaming paths. Only last hit always sidestep the dagger if shes just throwing it on caster minions. Play safe as usual
My biggest advice it is to not let her roam freely, plus with kat you don't have to kill her shes very feast or famine, just dont give her any kills and farm allawys keep your team aware to were she is and group after laning phase she really cant do muhc if she doesnt have a big lead by then
This needs lots of practice imo. I went against a kat as Orianna and still managed to die in lane with exhaust. Those kat players are typically one tick. I need to take nulifying orb next time for sure. I forgot about it. Btw, I joined orianna mains discord :D
