What kinds of work is your organization completing, and how many staff are working at different locations? This information is important. For example, if your organization is in the marketing field, it's possible to create a team and appoint a team leader who is responsible for employee attendance. You can assign targets to the team leader, specifying that they must achieve the set targets within a month. The pressure of meeting targets can motivate employees to be punctual and perform their job duties honestly.
If your organization is engaged in building construction or other infrastructural work, you can appoint an Administrative Executive who will be responsible for site administration, handling employees' grievances, managing the time office, and assisting in the smooth implementation of HR policies at the site. Another effective method is to install a biometric machine to monitor employee attendance and expedite the payroll processing.
There may be other ideas that our CiteHR friends can suggest to us.