If I understand you correctly, you want to filter the water to your regular faucet, on the cold water line. This is commonly accomplished with this kind of a housing
Pentek 158643 3G IB Slim Line #10 Clear 3/8" Housing with Pressure Release with a filter cartridge like this
CBR2-10 water filters for lead reduction and Ametek CBR210 carbon water filter 155268
This filter will allow plenty of flow for a single typical kitchen faucet.
Thank you,
WaterFilters.NET