While it would be easy*
to change Fiddler such that its generated Server certificates include the ClientAuthentication EKU, it doesn't really make much sense to do so. A client which expects the SERVER to have the ClientAuthentication EKU set in the certificate is supplies is buggy.
Having said that, I want to make sure that you're not mistakenly trying to use one of the Fiddler-generated certificates as a client certificate (e.g. by exporting it to ClientCertificate.cer)?
(*) In the upcoming v22.214.171.124+ versions of the Fiddler CertMaker add-on, you can set the fiddler.certmaker.bc.AddClientAuthEKU preference to true to add this EKU.
Check out the Telerik Platform - the only platform that combines a rich set of UI tools with powerful cloud services to develop web, hybrid and native mobile apps.