Is there a parameter that measures the quality of a split in cross validation in XGBoost?

In Random Forest Classifier, there is a parameter called ‘Criterion’ which measures the quality of a split (https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestClassifier.html)

Is there a similar parameter available in XGBoost?

No. GBM has its own measure calculated from the gradient.