Is it as he explained that he was only a victim of mafia extortion, or he actually had a deep relationship with mafia figures?

No, he had no deep relations. Like a lot of NYC developers, he had to deal with the mob. And he also dealt with them when he got into the casino business in AC. But anyone who's read the particulars of all this knows it was a handful of dealings. Say what you want about Trump but the idea he is mobbed up is nonsense.

http://jerseymanmagazine.com/bogus-claim-the-trumpmob-connection/

geogre a writes a good article on the claims that he was mob connected they are not true he was never deeply connected

He was never involved. The one guy he may have been friendly with at one point was John Stalluppi. That guy is a billionaire too.

He had closer ties to the Russian Mafia.

To be fair to Mr. Trump, he may not have been a willing participant. But I don't believe for a minute any developer doing anything that substantial was unconnected in the 70s and 80s. See "Concrete Club". Associate or not, Trump acts like a racketeer toward those who he owes money. Has anyone else read the story about the owner of Freehold Music in NJ who sold Trump $100K worth of pianos, and Trump beat him out of $30000 of it? Or the various contractors in Atlantic City who never got paid? I think Bayshore Rebar worked for him, I bet they got their money, though.

You can't be in the real estate business in NYC and not have some contact with the Mob.

Thank all of you for your answers.

Dealing with the Mafia when you are in real estate, construction, development, etc is just part of doing business here in New Jersey and in New York City, even now in the year 2016. I can't imagine how much worse it was in the 1980s.