There are two possible scenario,
If you application run on .net framework 4.5 or less than that and you can easily deploy new code to the production then you can use of below solution.
You can add below line of code before making api call,
ServicePointManager.SecurityProtocol = SecurityProtocolType.Tls12; // .NET 4.5
If you cannot deploy new code and you want to resolve with the same code which is present in the production, then you have two options.
Option 1 :
[HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\.NETFramework\v4.0.30319]
"SchUseStrongCrypto"=dword:00000001
[HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Microsoft\.NETFramework\v4.0.30319]
"SchUseStrongCrypto"=dword:00000001
then create a file with extension .reg and install.
Note : This setting will apply at registry level and is applicable to all application present on that machine and if you want to restrict to only single application then you can use Option 2
Option 2 : This can be done by changing some configuration setting in config file. You can add either of one in your config file.
<runtime>
<AppContextSwitchOverrides value="Switch.System.Net.DontEnableSchUseStrongCrypto=false"/>
</runtime>
or
<runtime>
<AppContextSwitchOverrides value="Switch.System.Net.DontEnableSystemDefaultTlsVersions=false"
</runtime>