In this paper, we consider the problem of fair scheduling of transactions of multiple types that are submitted to a permissioned blockchain system. Permissioned blockchains are being increasingly used for enterprise applications and by design are heterogeneous in nature, with different peer organizations performing different business functions. Transactions execute different smart contract operations that may have widely varying business importance. In such a setting, we argue that the typically adopted First-In-First-Out ordering mechanism for transactions in a blockchain system, which is a performance-limited resource, is inefficient and unfair. We propose a weighted fair queueing strategy for ordering transactions that can support differentiated quality of service for submitted transactions on the blockchain. The main challenge we address in this paper is to support fair allocation and differentiation in a decentralized manner, as there is no single authority that can facilitate this as in traditional systems. We demonstrate such a fair scheduling strategy and support multiple transaction types with different priorities on Hyperledger Fabric.