We report a search for neutrino oscillations to sterile neutrinos under a model with three active and one sterile neutrinos (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>3</a:mn><a:mo>+</a:mo><a:mn>1</a:mn></a:mrow></a:math> model). This analysis uses the NOvA detectors exposed to the NuMI beam, running in neutrino mode. The data exposure, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mn>13.6</c:mn><c:mo>×</c:mo><c:msup><c:mrow><c:mn>10</c:mn></c:mrow><c:mrow><c:mn>20</c:mn></c:mrow></c:msup></c:mrow></c:math> protons on target, doubles that previously analyzed by NOvA, and the analysis is the first to use <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>ν</e:mi><e:mi>μ</e:mi></e:msub></e:math> charged-current interactions in conjunction with neutral-current interactions. Neutrino samples in the near and far detectors are fitted simultaneously, enabling the search to be carried out over a <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mi mathvariant="normal">Δ</g:mi><g:msubsup><g:mrow><g:mi>m</g:mi></g:mrow><g:mrow><g:mn>41</g:mn></g:mrow><g:mrow><g:mn>2</g:mn></g:mrow></g:msubsup></g:mrow></g:math> range extending 2 (3) orders of magnitude above (below) <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mn>1</j:mn><j:mtext> </j:mtext><j:mtext> </j:mtext><j:msup><j:mi>eV</j:mi><j:mn>2</j:mn></j:msup></j:math>. NOvA finds no evidence for active-to-sterile neutrino oscillations under the <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mrow><l:mn>3</l:mn><l:mo>+</l:mo><l:mn>1</l:mn></l:mrow></l:math> model at 90% confidence level. New limits are reported in multiple regions of parameter space, excluding some regions currently allowed by IceCube at 90% confidence level. We additionally set the most stringent limits for anomalous <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msub><n:mi>ν</n:mi><n:mi>τ</n:mi></n:msub></n:math> appearance for <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mrow><p:mi mathvariant="normal">Δ</p:mi><p:msubsup><p:mrow><p:mi>m</p:mi></p:mrow><p:mrow><p:mn>41</p:mn></p:mrow><p:mrow><p:mn>2</p:mn></p:mrow></p:msubsup><p:mo>≤</p:mo><p:mn>3</p:mn><p:mtext> </p:mtext><p:mtext> </p:mtext><p:msup><p:mrow><p:mi>eV</p:mi></p:mrow><p:mrow><p:mn>2</p:mn></p:mrow></p:msup></p:mrow></p:math>. Published by the American Physical Society 2025