In a previously created Select list(Multiple choise) custom field, if we add a new option will this effect the previously created issues.
No.
Why would it? If you're adding an option to the possible list, there's no reason to assume you want to add it to the issues, and even if you did, JIRA has no way of knowing which ones you want to add it to. It's up to you to define what a new option should be added to.
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