We need to generate expenses - supplier wise report for a particular period

I'll be glad to help you track your Expenses.

To begin with, may I ask if you're trying to run an expense by the supplier? If so, we can run an Expense by Supplier Summary report. 

Here's how: 

1. On the left panel, navigate to Reports. 
2. Once done, search Expense by Supplier Summary.
3. From there, you can modify the date.

You can check this article to learn how to customize your reports: Customise reports in QuickBooks Online.

On the other hand, are you also trying to add a Cost Center in QuickBooks? If so, please know that this is currently unavailable. However, the system includes a project feature that allows you to track or quickly calculate your costs.

For further reference, please check out this article: Track hourly labour costs and profitability by project in QuickBooks Online.

Moreover, please let me know if you're trying to achieve something else or have a different concern.

Let me know if you have further concerns about generating expenses or any QuickBooks-related queries. Keep safe.