I have faced the similar issue for payment transactions. Issue resolved with only registry changes and no code change.
Web Instance(Server) is hosted in Microsoft Azure. Used .NET version 4.5. Using payment APIs for BPOINT & PayPal. Following are the registry changes carried out to resolve the issue:
Step 1: Enable TLS1.2 on Client and Server
REG ADD "HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\SecurityProviders\SCHANNEL\Protocols\TLS 1.2\Server" /v Enabled /t REG_DWORD /d 00000001 /f
REG ADD "HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\SecurityProviders\SCHANNEL\Protocols\TLS 1.2\Server" /v DisabledByDefault /t REG_DWORD /d 00000000 /f
REG ADD "HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\SecurityProviders\SCHANNEL\Protocols\TLS 1.2\Client" /v Enabled /t REG_DWORD /d 00000001 /f
REG ADD "HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\SecurityProviders\SCHANNEL\Protocols\TLS 1.2\Client" /v DisabledByDefault /t REG_DWORD /d 00000000 /f
Step 2: Disable TLS1.1 on Client and Server
REG ADD "HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\SecurityProviders\SCHANNEL\Protocols\TLS 1.1\Server" /v Enabled /t REG_DWORD /d 00000000 /f
REG ADD "HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\SecurityProviders\SCHANNEL\Protocols\TLS 1.1\Server" /v DisabledByDefault /t REG_DWORD /d 00000001 /f
REG ADD "HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\SecurityProviders\SCHANNEL\Protocols\TLS 1.1\Client" /v Enabled /t REG_DWORD /d 00000000 /f
REG ADD "HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\SecurityProviders\SCHANNEL\Protocols\TLS 1.1\Client" /v DisabledByDefault /t REG_DWORD /d 00000001 /f
Step 3: Enable Strong Cryptography for >NET framework
REG ADD "HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Microsoft\.NetFramework\v4.0.30319" /v SchUseStrongCrypto /t REG_DWORD /d 00000001 /f
REG ADD "HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\.NetFramework\v4.0.30319" /v SchUseStrongCrypto /t REG_DWORD /d 00000001 /f