The maximum message size quota for incoming messages (65536) has been exceeded

As per this question's answer

You will want something like this:

<bindings>
     <basicHttpBinding>
         <binding name="basicHttp" allowCookies="true"
 maxReceivedMessageSize="20000000"
 maxBufferSize="20000000"
 maxBufferPoolSize="20000000">
             <readerQuotas maxDepth="32"
 maxArrayLength="200000000"
 maxStringContentLength="200000000"/>
         </binding>
     </basicHttpBinding> </bindings>

Please also read comments to the accepted answer there, those contain valuable input.

If you are using CustomBinding then you would rather need to make changes in httptransport element. Set it as

 <customBinding>
    <binding ...>
     ...
     <httpsTransport maxReceivedMessageSize="2147483647"/>
    </binding>
 </customBinding>

You need to make the changes in the binding configuration (in the app.config file) on the SERVER and the CLIENT, or it will not take effect.

<system.serviceModel>
    <bindings>
        <basicHttpBinding>
            <binding maxReceivedMessageSize="2147483647 " max...=... />
        </basicHttpBinding>
       </bindings>
</system.serviceModel>

Updating the config didn't work for me, but I was able to edit the binding programmatically:

private YourAPIClient GetClient()
{
    Uri baseAddress = new Uri(APIURL);

    var binding = new BasicHttpBinding();
    binding.MaxReceivedMessageSize = 20000000;
    binding.MaxBufferSize = 20000000;
    binding.MaxBufferPoolSize = 20000000;
    binding.AllowCookies = true;

    var readerQuotas = new XmlDictionaryReaderQuotas();
    readerQuotas.MaxArrayLength = 20000000;
    readerQuotas.MaxStringContentLength = 20000000;
    readerQuotas.MaxDepth = 32;
    binding.ReaderQuotas = readerQuotas;

    if (baseAddress.Scheme.ToLower() == "https")
        binding.Security.Mode = BasicHttpSecurityMode.Transport;

    var client = new YourAPIClient(binding, new EndpointAddress(baseAddress));
    return client;
}

You also need to increase maxBufferSize. Also note that you might need to increase the readerQuotas.