Well, as someone who mains zed, i can give you Intel on his weaknesses which you can abuse, exploit, or share with your teammates to have him dealt with.
Since you are an AP midlaner main, i will try to pinpoint my tooltips towards AP playstyles and itemizations.
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Zed has arguably the weakest 1v1 potential against champions pre 3. At lvl 1 and lvl 2 you as taliyah are highly advised to go E W first to harrass him very hard, unless he goes for W at lvl 2 in which case when you pointed on E take Q for Level 2
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Zed, despite being very mobile, is a predictable champion when it Comes to positioning. When he casts R, he will appear behind you in melee range. When he swaps, he will appear exactly where his shadows are and not anywhere else. Lock down his escapes with your jungler by zoning his shadow, forcing him to overextend and create a chase that favors you. Place your Taliyah E's infront of you if you notice he is approaching and save your W for either his swap or his R reappear post 6 to throw him right into your Mines.
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Rush zhonyas first item. Against zed you Need a stasis since you are an rather immobile mage with no innate defences (except maybe the W).
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Roam a lot. If your lane vs zed is indicatory lost, do not try to pressure it back. create pressure elsewhere which will force him to counterroam. That, in turn, allows you and your jungler to set up traps to corner him in unfavorable fights.
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Safe your Flash for his ult. Flash only after he appears next to you, and try to flash over to positions and places where he cannot garuanteedly kill you. behind teammates or creeps even. His Q deals less damage if it hits you as not-the-first target which in turn makes his R damage weaker on the Pop. The reduced damage gets additively reduced by another 25% for any shuriken other than the first.
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Fight on Populated areas. Just as the previous tooltip says, zed's damage is massively mitigated if it does not hit a single target. Fight inside your creep wave to cut off his Q damages which could very well save your life
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Be safe. Pre 6 zed cannot effectively all out unless you are low health because then he can proc his passive which deals about as much Magic damage as an AA could, which earlygame is a LOT. Keep trades short and ranged as good as you can.
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Learn to zig-zag. Zed's Patterns and combos are very predictable since he has only 2 direct damage spells from which one is a self-multiplicatory skillshot. If he throws his W out, immediately walk away from it so he cannot combo you without swapping in.
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Dodge his E on his shadow. it only slows if his shadow applies it, not he himself. When you are not slowed zed will have a much harder time hitting his Q shurikens. Try also to make your movements unpredictable. The longer he takes to Q, the lesser his chances to hit them.
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Always ward. Zed is an assassin that can literally jump over walls with a blink to kill you. Always Keep your area widely visioned and stay close to nearby allies. Zed Players, ecspecially the newer ones will greed the hell out of lone split pushers.
I hope These sets of weaknesses will be able to help you out somewhat, and if not, well screw me then.
Edit: I forgot to mention.
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Abuse his cooldowns. Zed earlygame has an over 20 second cooldown on his W. meaning his trading breaks are insanely long, whereas you as taliyah have mildly assumed half his cooldowns. Trade him when his shadow is on cooldown or bait him into abusively wasting it so he is easily ganked.
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Let him push. Zed's waveclear depledes his entire combo, ecspecially early on, meaning if he wants to push wave he sacrifices his kill pressure. Build your advances around those Windows of time