Are paid links illegal?

Illegal ? 

Well you won't go to jail for buying links 😀 Sorry that made me smile, 

Buying links is fine, there is no difference between a advert for your site (which is paid for) and a link. The difference though is all adverts should have the tag rel="nofollow". 

I suspect though you mean buying follow links and doing this in bulk in order to gain in SERPS. This is of course frowned upon by search engines as its a clear signal your attempting to manipulate your position by posting links to your site. It is also very easy to spot as suddenly a load of links appear within a short space of time. Your backlink profile would see a spike which would trigger it to be looked at more closely. 

In the old days this would mean a human inspecting your backlink profile, however google have since matured and can do this automatically now and often you will see your position drop instead of rising because of a penalty automatically applied to your site. 

Adverts on the other hand are posted for traffic and therefore are typically ignored by google from a ranking point of view. You are welcome to post as many adverts as your budget allows but make sure they are of the no follow type. 

paid links are not liked by google but it doesn't mean that anyone is going to sue for that or a criminal offense is going to be filed against you.

NOt illegal but aganst google standards

paid links are not liked by google but it doesn't mean that anyone is going to sue for that or a criminal offense is going to be filed against you. Thank you! 

<snip - no self promotion>

no not at all.paid links also getting high rank in SERP

<snip - no self promotion>

No they are not. Read this - https://moz.com/blog/nofollow-sponsored-ugc

No, paid links are not illegal. Paid links increase your website traffic instantly. This gives instant traffic.

This question about link buying, which is a black hat SEO tactic that goes against Google’s webmaster guidelines and will result in a penalty if you're found. First, while there’s no law against it, Google is free to do whatever it wants to those that break its guidelines. They are an independent ruler of their (pun planned) domain. So if they find you violating their guidelines, they can remove your website from the results. That means no traffic for you, no leads, and no sales.