A good solution is to have connectionstring set up part as IOption or something similar like binding configuration to some object and then contructor-injecting this object to a class which contains method acting as recurring job.
Example:
public StatusJobs(DbOptions dbOptions)
{
_dbOptions= dbOptions
}
[DisableConcurrentExecution(timeoutInSeconds: 20)]
[AutomaticRetry(Attempts = 0, OnAttemptsExceeded = AttemptsExceededAction.Delete)]
public void DoSmth()
{
//dbOptions avalaible here
}
Also, it would be better to inject some connectionfactory instead of connectiostring.