BibLaTeX is an alternative implementation for how references are managed and typeset in a LaTeX document. There are various bibliography engines that support this implementation, including the established BibTeX engine.

However, BibLaTeX uses Biber as its default backend engine. Biber is an engine that is currently incompatible with TexpadTeX. We plan to implement the Biber support in future but until then BibTeX may be used as the backend by explicitly specifying it in the biblatex package include statement as shown below,

\usepackage[backend=bibtex]{biblatex}

This allows TexpadTeX, or more specifically its bibliography engine TexpadBib to handle the bibliography compilation. Following is a full example comprising a .tex file with LaTeX source and a .bib containing bibliography entry

\documentclass{article}
\usepackage[backend=bibtex]{biblatex}
\bibliography{bibliography}
\begin{document}
Citing reference: \cite{ref1}
\printbibliography
\end{document}

@article{ref1,
  title={1999 Paper},
  author={Doe, John},
  journal={International Journal of Nonsense},
  year={1999}
}

This is supported across Texifier macOS and iOS.

If you must use the default Biber engine, the external typesetter is the only way currently. On macOS, this will involve installing and using a TeX distribution such as MacTeX.