support
playing one of the 2 roles known for taking all of the blame
I am doing my job perfectly
You're not even lvl 30 I'm sure you still have a lot to learn about the support role c:
as a support but if my skills are on cooldown
Why are your abilities on CD? Your job is to peel your your ADC. You should have your abilities up until the moment your ADC needs to be saved and then you use your abilities as needed. As such the only time your abilities should be on CD is at the end of a long engage. At that point nobody should be able to get mad at you for not shielding them because you just did shield them. Nobody should be able to get mad at you for not stunning them because you just did stun them, etc.
or you know the enemy isn't in target range
That is probably 75-95% your fault. Positioning is the most important part of your role. Unless your ADC has a dash and uses their Dash + Flash to get ahead of you, you should be in range to protect them. Your job 100% is to save your ADC unless they can't be helped and then your job is to peel for your APC (the midlaner). The enemy should not be in range to harm your ADC if you are not in range to save them.
or even no mana
That normally means you're spamming too much (and/or you are building wrong). When you said above that your skills are on CD and then you say you might not have mana those are indicators of carelessly using your abilities or wasting your item slots.
and let me play support the way I play it or they can ask me to leave
The support role is a team oriented role. It doesn't matter if you think what you're doing is the right choice if you notice your ADC isn't following up when you go to ult or when you do X that they are upset about, then you aren't going to get the follow up you need by playing "your way". You want to avoid fighting as well as waste in the botlane. Wasting abilities because you aren't in sync, fighting with each other and letting the enemy botane get ahead. If your ADC isn't comfortable with what you're doing you need to just stop. Play their way for 15-20 minutes, and then if you disagree with them and think what they're doing is stupid just focus on protecting a different carry in teamfights.
The biggest thing is there is no "your way" to play botlane, it has to be "our way" we have to play "together" and if you're being stubborn then you don't deserve to luxury of being in the duo lane. I'm sorry but a person like me preys on supports who want don't want to synchronize with their ADC because I know that their ADC won't be able to back them up when I catch them out or that you won't be close enough by to save your ADC when I pounce on them. I know if you guys aren't 1 unit you're just that much easier to tear apart.
If I get ban from league then it will be okay since the bullies are not gonna be dealt with anyway.
you didn't really prove that they were bullying you. You basically just said that they were disagreeing with how you play and you left because you felt bullied that they weren't letting you play a team game your way. If you want actual tips and you want someone to tell you why they are "bullying" you feel free to add me in game and we can play a norms or two together and I'll tell you what you can do to convince your ADC to play closer to your way as well as what you can do to play more towards your ADC.