Client Authentication using a certificate without private key in Xamarin.iOS

I should make a post request with client authentication using the certificate located on an electronic card in Xamarin.iOS.
The problem is that the certificate private key cannot be extracted but through an APDU request it is possible to use the method to sign.
How can I start a client authentication challenge with the certificate without private key and use the APDU request to sign the connection?
I tried to extend the RSA and X509Certificate2 classes with the HttpClient, HttpWebRequest, NSUrlConnection and NSUrlSession libraries but I failed.

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