Permissioned Blockchain has become quite popular with enterprises forming consortium since it prioritizes trust over privacy. One of the popular platforms for distributed ledger solution, Hyperledger Fabric, requires a transaction to be endorsed or approved by a group of special members known as endorsers before undergoing validation. To endorse a transaction, an endorser mentions its identity along with the signature so that it can be verified later. However, for certain transactions, difference in opinion may exist among endorsers. Disclosing the identity of an endorser may lead to conflict within the consortium. In such cases, an endorsement policy which not only allows an endorser to support a transaction discreetly, but at the same time takes into account the decision of the majority is preferred. Thus we propose an Anonymous Endorsement System which uses a threshold endorsement policy in order to address the issue. To realize a t-out-of-n endorsement policy, using any of the existing threshold ring signature for our endorsement system would have violated the privacy of endorsers as either the identity or the secret key of the endorsers get revealed to the party who recombines the signature after collecting each signature share. All these factors motivated us to design a new ring signature scheme, called Fabric's Constant-Sized Linkable Ring Signature (FCsLRS) with Transaction-Oriented linkability for hiding identity of the endorsers. We have implemented the signature scheme in Golang and analyzed its security and performance by varying the RSA (Rivest-Shamir-Adleman) modulus size. Feasibility of implementation is supported by experimental analysis. Signature and tag generation time is quite fast and remains constant irrespective of change in message length or endorsement set size for a given RSA modulus value, assuming all the endorsers generates their signature in parallel. Each verifier is required to count and check individual valid ring signature. If the aggregate is above the threshold value, stated by the endorsement policy, then it confirms that the transaction is valid. This increases the verification time depending on the threshold value, but has very little effect on the scalability since generally $t<<n$. Lastly, we also discuss the integration of the scheme on v1.2 Hyperledger Fabric.