Zhivko,
It looks like you are measuring right at the FET gate. You might be experiencing shoot-through due to impedance between the gate drive output and your FET gate. Even though our device tries to protect from shoot-through, the chip will "think" that the FET is off, but the FET is not fully turned off because the gate hasn't fully discharged. My picture below shows a modified test setup to help confirm this. If you probe at the device GHA pin and at the FET gate, I expect to see two different signals.
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From the schematic you posted on the previous post, I saw that you have some resistors in the gate drive path that impact the way the gate discharges. One thing you can do is remove the gate-to-ground resistor and make the resistor in the gate-drive path 0-ohm. This should solve the problem, however, you may want to check to make sure the overshoot/undershoot voltage on the gate drive trace is acceptable for the DRV8302 and the FETs your are using. This overshoot/undershoot comes from package and trace parasitics.
If possible in future layout revisions, keep the traces between the gate drive outputs and the FET gates as short as possible.
If you want to leave the resistors in the circuit, follow the guidelines in the app note Fundamentals of MOSFET and IGBT Gate Driver Circuits. R_GATE is calculated on page 15. You can put a diode in parallel with it (section 3.4.1). Designing the Rgs resistor is described in section 3.5.
Because the INxx pins have internal pull-down resistors, you can leave the unused ones unconnected.