Want to add lock (can't modify apartment)?

Well, right off, you can't do that because that is modifying existing structure.   A door wedge is highly effective, so is a leaning wooden chair back under door knob.  Then again it is a steel door so you could get an arc welder and weld the door shut, meaning you need an angle grinder to cut it open.  I am in the "crazy zone"  You will find you are not that important to anyone else.  That is the truth of the matter.

Of course they have other keys.  One to laundry room, one to apartment, one to the front door, one to the garbage bin, a few to the car, some to their  MOM's house. One to their bicycle.

None of the other tenants have a master key.  Only the LL has that just in case of a flood or fire coming out of your apartment then they bust in and put it out...or stop the flooding.  They have no other reason to enter your apartment EVER.   

. Don't you READ your contract with the LL?   This is stuff he loses in Court if he trespasses into your apartment.  Seriously. It is a B&E. Even if you were growing WEED, he can't do a damn thing except give you a 48 notice that he wishes to inspect you unit for some reason (ALSO WRITTEN IN THE CONTRACT)  He can't make up schit when he feels like it.

"I can't prove, but already seen it."   That is so weak you will be laughed out of court.   Since "when" do you know about who other tenants hang with? And who are buddies and even loan keys to their friends because they party together.

YOU KNOW NOTHING.  PEOPLE HANG AROUND TOGETHER. All , except you.

If you just want to lock it better while inside, which is certainly your legal right, use a floor wedge or maybe a travel lock that slips into the latch striker plate with the door open, then fits against the in-swinging door when you close and lock it. It doesn't require any tools or permanent holes, since the striker plate already has a hold for normally receiving the latch-bolt.

As suggested by others, you also have the legal right to view and record the images of anyone entering your home at any time.  Some laws may limit the legal right to record their voices secretly, so you'd need to look up the local laws if you want to do that without risking a felony.

There are many other "temporary interior locks" available, including "night-bars" that jam between the doorknob and a friction point on the floor inside the door.  Google "portable door locks" and find lots of options for under $20.

Use the sort of system recommended for travellers in hotels - a simple door wedge that stops the door opening when you are there. You cannot do much about when you are not there. You could have a nanny cam to see who goes in and out if that is important to you.

Door wedge when you are home, a magnetic sign that your place is protected by the second amendment might deter a few creeps.

You're over thinking in the wrong direction.  Just Google door hammer and choose the option you like best.  There are many kinds that work great and require NO installation.

your lease does not allow that -- landlord has to have access for possible emergency maintenance purposes.  you may use a brace under the doorknob inside the apartment while you are in there.

If you rent, it is ILLEGAL to add a lock without the landlord's permission. Any magents strong enough to be useful needs to be attached in a manner that requires holes.

A simple door wedge will work remarkably well while you're inside. There are other more high-tech door jammers available too.

I just want added security, while in apartment.