Yes, you can configure user permissions per individual jobs.
Jenkins allows you to give different permissions to a user across different jobs,using "Project-based Matrix Authorization strategy".
Follow the steps to do this, 
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 From the jenkins dashboard,click on Manage Jenkins.
 
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 under Manage jenkins->Configure Global Security->select Enable security.
 
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 Under the Authorization section, select the "Project-based Matrix Authorization Strategy"
 
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 Add the particular user and assign the appropriate permissions.
 
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And then to assign Job specific permissions :
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Go to the job (say job1) for which you need to assign permissions.
 
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Click Configure->under the general tab->Enable Project-based Security.
 
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 Add the particular user (say user1) and assign the required permissions.
 
 
This is useful when specific jobs shouldn't be accessed by certain users.