I've seen several times that every altcoins doubles the price in a single day which means every coin or token has its opportunity to boom.
No. This is a wrong conclusion.
The reason of rising in price is only demand/supply ratio. If there is a sudden rise and a sudden fall it means the rise was inorganic/manipulated.
If there is a slow rise it means there is organic growth, people are buying because they believe this will be going up.
For altcoins the first statement is almost 100% accurate. If there is sudden rise, it is a pump and dump going on. This is a bad omen for the long term and you should exit it before it dumps.
IF BTC price does down they drop but suddenly they skyrocket by the next day itself, it's pretty hard to judge which coin might pump for the next day.
Now this is a different topic. Bitcoin is followed by altcoins is a common phenomena. But there is no such indicator or metric to judge whether it will move up or down, usually they follow bitcoin.
Is there any specific website which might help me to identify?
No. Also stop depending upon websites for such information. Use the charts if needed from websites but dont look for identifying when to buy or sell. That should be done by you and only you. I am saying this only to stop you from falling prey of fake signals groups which are a part of a scammers guild.