Peltier module voltage drop
Facts: -


The TP4056 can supply up to 1 amp at up to 4.2 volts
The MT3608 starts to hit the end-stops when supplying currents of about 1 amp
The Peltier module has a resistance of about 2 ohms



  Why does that happen and how can I get the Peltier to be fed with the
  original output of the converter of 6v?


So, any voltage across the peltier greater than about 2 volts will result in the TP4056 and MT3608 being unable to supply enough current. Either or both will cause a problem.