This is not an action or a maneuver, and can cause the ship to overlap obstacles (but not other ships). The ship suffers the effect of any obstacle it overlaps.

well, When say << The ship suffers the effect of any obstacle ir overlaps>> means that just after you move the enemy ship it suffer the :

Asteroid: rolls one attack die. On a crit result, the ship suffers one damage; on a hit result, it suffers one critical damage. While a ship is overlapping an asteroid, it cannot perform any attacks.

or if the enemy attack first have no effect "becouse enemy do the Perform action on the activation phase, and attacks befor you move him "at less no more than -1A, and the next turn if if its maneuver template overlaps that obstacle token enemy skip its “Perform Action” step this round. After skipping the “Perform Action” step, it rolls one attack die. On a hit result, the ship suffers one damage; on a crit result, it suffers one critical damage.

and if overlapping an asteroid, it cannot perform any attacks too.

another think:

RULES REFERENCE:5

A ship cannot barrel roll if it would overlap another ship or an obstacle token, or if the maneuver template would overlap an obstacle token.

TRACTOR BEAM RULES:

This is not an action or a maneuver, and can cause the ship to overlap obstacles (but not other ships).

sow you can do the barrel rol over a obstacle

RULES REFERENCE:

• A ship cannot barrel roll if this would cause the ship to flee the battlefield.

sow you cant do the barrel rol on the enemy if it cause the ship fleet the battlefield, but if enemy its on a bad position maybe we cant do eny moneuver to prevent fleet the battlefield.

Was there a question in there somewhere?

Yes, a ship that you tractor beam onto an asteroid will roll for damage and can't shoot, and onto a debris field rolls for damage and takes a stress.

Tractor beam moves ships onto obstacles because it specifically says it can. Cards override the main rule book when they specifically allow something the rules don't. Rules Reference Page 1 under Golden Rules. Because Tractor Beam does not specifically allow you to, you can't use it to barrel roll/boost someone off the board.

And yes, you can't roll or boost something off the board even with a TB, but you can roll or boost them such that they can't stay on the board with their next manoeuvre.

Was there a question in there somewhere?

well, When say << The ship suffers the effect of any obstacle ir overlaps>> means that just after you move the enemy ship it suffer the :

Asteroid: rolls one attack die. On a crit result, the ship suffers one damage; on a hit result, it suffers one critical damage. While a ship is overlapping an asteroid, it cannot perform any attacks.

or if the enemy attack first have no effect "becouse enemy do the Perform action on the activation phase, and attacks befor you move him "

there, the damage when you move him or on his Perfom action fase, sow never ... move first, then attacks ..

I think the answer is "yes".

If your tractor beam attack moves the enemy ship so it overlaps an obstacle, the enemy suffers the same effect as if it landed there after its own manoeuvre.

Moving the enemy onto an asteroid is less useful if they have already attacked at a higher PS. It can still be a good thing to do, particularly if their manoeuvre template will overlap the asteroid next turn and they have to roll for possible damage again.

If you tractor beam someone onto an asteroid, they roll for damage. They cannot shoot, though if they've already shot this round that may not make a difference.

If you tractor beam someone onto a debris field they gain a stress and roll for damage taking only the [kabooms] results.

Next round they may or may not be affected by the obstacle depending on how their activation phase works out.