I am sorry for mistake but I thougth that it is not necessary because there are not the current limiting resistors set to bases at this main circuit. I will put 1K resistors.

 

That's probably what damaged the BD139-140 transistors.
That drawing is not a detailed schematic.

 

The previously pictured Piezo-Tweeter will have a maximum Output at around ~6kHz,
this is probably too high of a Frequency to make a good Alarm-Noise.

There is a larger version Piezo-Tweeter, which is also very common, which is 2-inches X 6-inches,
which has a much higher Output, and can create noises down to ~2kHz.
It would be a much better choice for an Alarm-Noise-Maker, and
it can withstand higher Voltages without burning-up.
The smaller Tweeter may not last more than ~5-minutes or so
when being driven with a Bridge-Amp Square-Wave at ~12-Volts.

If You want serious Output, You need a serious Speaker with much more efficiency.
A Re-Entrant-Horn-PA-Speaker will deafen You at ~1khz.
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If I decide to buy that serios speaker from the picture can you reccommended me the NPN and PNP transistors for my H-Bridge that are sutable for that power load?

I found them at link:
https://www.mgelectronic.rs/horn-sirene
They are all 12V DC

Can they be connected to this H-Bridge these circuits?

 

 

A Piezo-Tweeter "acts-like" a small Capacitor.

A Re-Entrant-PA-Horn has a Magnet and a Wire-Wound-Voice-Coil,
usually with an Impedance of ~8-Ohms.

The Piezo-Tweeter will draw more Current as the Frequency gets higher.

The Re-Entrant-PA-Horn will draw more Current as the Frequency gets lower,
that is, below the resonant Frequency of the Horn,
which is determined by the Length of the Horn,
which is approximately 2.5 X the overall physical Length of the Horn-Assembly,
which for a ~6-inch long "Body", would be approximately ~15-inches.

A Wavelength of ~15-inches equates to a lowest "safe" Frequency of approximately 900Hz or 0.9kHz.
Operation below 900Hz will over-stress both the PA-Horn and the Amplifier,
and protection against this low-Frequency possibility must be used.
All that is required for this is a special Speaker-Crossover-Capacitor with
a value of approximately 22uF. Crossover-Capacitor

Since the PA-Horn draws substantially more Current than the Piezo-Tweeter,
the proposed BJT Transistors will NOT be adequate.
I would recommend some very over-rated MOSFET-Transistors such as .........

2X AOTF266L 785-1443-5-ND
and
2X AOTF4185 AOTF4185-ND
There are, of course, many other part-numbers that would work just fine,
but, both of these numbers are TO220-Full-Pack,
completely insulated Packages which are very convenient for mounting.
They must be mounted to a piece of Aluminum, or an Aluminum-Box for Heat-Sinking.

I would also recommend a different wiring of the 555-Chip to insure a ~50% Duty-Cycle-Square-Wave.
Only one 555 is needed, plus one small FET to provide an inverted Output-Signal.
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