quad attack and focused damage

[bulat_fbi]

Hi! I managed to make operative(15 lvl)/solder(5 lvl) character.
Operative give us quad attack - So it is a full attack , but we can fire 4 times with negative bonus of -4. One of Solders option give us focused damage, which reduce penalty of both attack rolls of regular full attack from -4 to -3.
will focused damage reduce penalty of every attack roll if we have Quad attack?

[Samantha DeWinter]

I assume you mean Focus Fire, not Focused Damage. Text as written:

Focus Fire (Ex) - 5th Level
When you make a full attack with a ranged weapon, you can make both attacks with a –3 penalty instead of a –4 penalty as long as they both target the same creature. If your first attack kills or knocks out the target, you can instead make the second attack against a different creature at a –4 penalty. Once you have the soldier’s onslaught class feature (see page 112), you can use this ability with it, making three attacks against the same creature at a –5 penalty; if your first or second attack kills or knocks out your target, you can make your remaining attacks against a different creature at a –6 penalty.

As it specifically calls out Soldier's Onslaught and has special limitations for it, I do not believe it would give any bonus to other full-attack types like Quad Attack.