How to limit characters in Academica featured posts widget?

I am guessing that this is the theme you are talking about. If so, I don’t see any specialized filters that would let you alter the character count of the excerpt. The widget does use get_the_excerpt() so you should be able to alter the character count with Core filters though.

function excerpt_trim_cb_wpse_114219($excerpt) {
  remove_filter('wp_trim_excerpt','excerpt_trim_cb_wpse_114219',1000);
  return substr($excerpt,0,5);
}
function insert_into_sidebar_wpse_114219($s) {
  if (
    isset($s['callback']) 
    && is_object($s['callback'][0])
    && 'Academica_Featured_Posts_Gallery' === get_class($s['callback'][0])) 
  {
    add_filter(
      'wp_trim_excerpt',
      'excerpt_trim_cb_wpse_114219',
      1000
    );
  }
}
add_action( 'dynamic_sidebar', 'insert_into_sidebar_wpse_114219' );