I suspect the ignition switch too , how can I verify that it fault ?

Another thought that I have done in a pinch to get a vehicle back is to use a fused wire (a wire with a in your case 10 amp fuse in it) from the battery or 12 volts (what ever was easiest to access) and use it to power the trans fuse. There should be 12 volts (battery power) at the trans fuse. The Trans fuse gets it'* power from the ignition switch.Trans fuse also feeds power to the instrament cluster

You know what is the color of the wire that provide 12v from the ignition to TRANS fuse ?
if I find I disconnect it from the ignition and connect to another 12V . Also I use the TRANS fuse itself this way .

I don't have a schematic available now,but as I remember any Orange,Red,and Pink wire at the ignition switch should be 12 volts. with the key on. That connector I believe is on the steering column. Connector has 2 long single row connectors top and bottom and 1 multi row connector in the middle. The middle connector is from the ignition switch.

You can remove the trans fuse and put a wire attached to 12 volt power and put in where the trans fuse goes on the fuse out put side. If you remove the fuse, the fuse terminal with power with the key on is from the ignition switch. the fuse terminal that has no power with the key on is the fuse output "load"side. attach the 12 volt power wire to the fuse terminal that does not have power with the key on. Road test and see what happens.

Update :
I did what you told me , disconnect the fuse and measure the volt inside the fuse pin . One 12V the second 0V (because it is the output) , but in the input I get 12V .
when I connect the fuse again it drop to 4V .
what could be the reason ?

Disconnect the connector on the transmission and see if the voltage drops. If it stays at 12 volts there could be a shorted solenoid or harness in the transmission. Have see both issues puling down the circuit voltage.
Also put a test light with a bulb in it (or even a head light bulb would be better due to higher amp draw) and attach on side to ground and the other end to your circuit at the trans fuse input side and make sure it lights up. This will test to make sure there is enough Amperage to power the Circuit. This can also be done at the trans connector by using a pin into the connector . This would test to verify that there is enough Amperage getting to the trans. The light will "Load" the circuit. If there were to be a corroded wire it could carry or show 12 volts but would restrict the amperage needed to power the circuit.

I disconnet the connector from the transmission . I open the connector and measure with voltmeter the E pin . It shown the same voltage in the fuse (4V) .

this pink wire goes to the PCM or directly to the fuse box ?

I reread your last comment. With a light bulb from the fuse input side (terminal powered by ignition switch) and the other end to ground the light should light bright. If not, the ignition switch could give you 12 volts no load and drop due to the load on the circuit. Switch not passing sufficient amperage. Did you try putting your temporary power wire to the other terminal of the trans fuse (fuse output side) and what was the result ?

Pink wire at E terminal of the trans connector goes to the fuse box