XGB custom objective function - small change to default regression squared error objective function
You can find a good explanation and example on creating a custom objective function here:
https://xgboost.readthedocs.io/en/latest/tutorials/custom_metric_obj.html
https://github.com/dmlc/xgboost/blob/master/demo/guide-python/custom_objective.py
https://github.com/dmlc/xgboost/blob/master/demo/guide-python/custom_rmsle.py
Original XGB code repo is here, you may have to do some digging to find the code for your objective function:
https://github.com/dmlc/xgboost