How can I use Crypto APIs to sigh hash for TLS 1.2

Question

I am working to upgrade TLS version form 1.0 to 1.2 for existing windows/Win CE application. Right now my application is using Openssl 0.9.8k(supports TLS 1.0). To upgrade TLS version I am using Openssl-1.0.2p(supports TLS 1.2). I was signing data using MD5-SHA1 similar to steps followed in MD5-SHA1 hash using CryptoAPI (my requirement was same as this)

1. Created hash using Certificate key handle provider and use CALG_SSL3_SHAMD5 algorithm.
2. Using CryptSetHashParam, I set the initial hash value
3. Signed the hash using CryptSignHash.
4. After that, reverse the bytes order (as OpenSSL signature is Big endian mentioned.

But TLS 1.2 has to sign hash using RSA-SHA256. How can I achieve using Crypto APIs?

I have tried to Created hash using Certificate key handle provider and use CALG_SHA_256 algorithm instead of CALG_SSL3_SHAMD5. But Certificate verification failed at server with error as "Bad Signature".

I have been surfing MSDN pages and I assuming that CNG APIs can do my Job for Windows 7 OS. If it is true, How can I achieve? Also I am not seeing CNG equivalent APIs in Windows CE, How can I achieve in Windows CE?

Thanks.