Issue With Authenticating Request To the WordPress API

We have built a woocommerce integration for our platform, we ask the users to generate a pair of consumer key and consumer secret to authenticate our requests to their woocommerce instance . When authenticating requests over https , some customers request get authenticated with http basic auth while others with query param auth. My question -> Is there a single way to autheticate requests over https irrespective of that the ssl is configured correctly at the client’s server or not.