Calling funcions :>

When you use INPUT_PULLUP the pin reads HIGH when nothing is connected to it. When a button connects the pin to Ground it reads LOW. I think you have your logic backward.

#include <Servo.h>
const byte Button1Pin = 12;
const byte Button2Pin = 13;
const byte SerwoPin = 2;

Servo serwo;

const int pozycja = 90;/ /1st position of servo 0-180 pozycja+=position
const int mgora = 130;
const int gora = 170;  //positions of servo
const int mdol = 40;
const int dol = 10;

void setup() {
  Serial.begin(57600);
  while (!Serial);

  serwo.attach(SerwoPin);
  serwo.write(pozycja); //default setting of serwo : 90 stopni

  // pinMode(2, OUTPUT); //servo output
  pinMode(Button1Pin, INPUT_PULLUP); //button input
  pinMode(Button2Pin, INPUT_PULLUP); //button input
}

void loop() {

  // If button2 is NOT pressed, go to mgors?
  if (digitalRead(Button2Pin) == HIGH) {
    serwo.write(mgora);
  }

  // Then if button1 is NOT pressed, go to mdol?
  if (digitalRead(Button1Pin) == HIGH) {
    serwo.write(mdol);
  }
  else // Button 1 is pressed
    // If both are pressed, go to pozycja?
    if (digitalRead(Button2Pin) == LOW) {
      serwo.write(pozycja);
    }
}