readthedocs-sphinx-search is a Sphinx extension to enable search as you type for docs hosted on Read the Docs. Try it at https://readthedocs-sphinx-search.readthedocs.io/en/latest/?rtd_search=testing.

pip install readthedocs-sphinx-search

Add this extension in your conf.py file as:

extensions = [
 # ... other extensions here
 'sphinx_search.extension',
]