The study investigates the task of authorship attribution on short texts in Slovenian using the BERT language model. Authorship attribution is the task of attributing a written text to its author, frequently using stylometry or computational techniques. We create five custom datasets for different numbers of included text authors and fine-tune two BERT models, SloBERTa and BERT Multilingual (mBERT), to evaluate their performance in closed-class and open-class problems with varying numbers of authors. Our models achieved an F1 score of approximately $0.95$ when using the dataset with the comments of the top five users by the number of written comments. Training on datasets that include comments written by an increasing number of people results in models with a gradually decreasing F1 score. Including out-of-class comments in the evaluation decreases the F1 score by approximately $0.05$. The study demonstrates the feasibility of using BERT models for authorship attribution in short texts in the Slovenian language.