A 3 switch configuration has:
- 3-way switch with hot and two travelers. You may have neutral in the same box, or you may not, depending on how the circuit was wired.
- 4-way switch two 2 sets of 2 travelers. There will be a 3rd wire in each cable. That 3rd wire will be the same wire in both cables and wire-nutted together. That wire could be neutral or hot or switched hot.
- 3-way switch with switched hot and two travelers. You may have neutral in the same box, or you may not, depending on how the circuit was wired.
Based on the picture, this switch is one of the 3-way switches and has white marked as black, making that white wire
not a neutral but either hot, switched hot or a traveler - impossible to guess a traveler because the convention is one black screw for common and two brass screws, so the blackened white wire must be on a brass screw (since the picture shows the black wire on the black screw). (Thank you FreeMan.) But that means that most likely the necessary neutral for a smart switch is not in this box.
It is possible that the other 3-way switch (but not the 4-way switch, based on what I can guess from this 3-way switch) will have neutral available in the box. It is also possible that the other 3-way switch has a 2-wire cable with hot and switched hot to the light fixture and not have any neutral at all. Need pictures of the other box, showing how the switch is connected and all other wires/cables in the box to know for sure.
Note that some smart switches for use with 3-way/4-way switch circuits use a "smart" device wired at each switch location, some use a "smart" device only at the first location with conventional switches in the other locations, and some use a "smart" device wired at the first location and non-wired remotes (battery operated) at the other locations.