First, delete certificate without private key from keychain - it is useless and may generate errors in future.
Open your keychain access and generate certificate signing request (In top menu go for Keychain access -> certificate assistant -> request a certificate from signing authority). You should see this window
Select saved to disk, and enter your email address. CA email address leave blank.
Specify location of generated certificateSigningRequest file wherever you want. Then go to Apple developer member centre and create development certificate. Proceed usual procedure, select iOS app development, specify your created csr file, generate, download, add to keychain. Profit=)