I'll help you create a basic structure for a billing app similar to Vyapar with both online and offline functionality. We'll use Next.js for the frontend and backend, and implement offline capabilities using IndexedDB. Here's a starting point for your app:

This is a basic structure for a billing app with online and offline functionality. Here's an overview of what we've created:

1. A main BillingApp component that manages the state of invoices and handles online/offline status.
2. An InvoiceForm component for adding new invoices.
3. An InvoiceList component for displaying existing invoices.
4. Offline storage using IndexedDB (via the idb library) to store invoices locally.
5. Online synchronization using a simple API route.

To make this a full-fledged billing app like Vyapar, you would need to add more features such as:

1. User authentication and authorization
2. More detailed invoice information (e.g., individual line items, taxes, discounts)
3. Customer management
4. Product/inventory management
5. Reporting and analytics
6. PDF generation for invoices
7. Multi-currency support
8. Data backup and restore functionality

You would also need to implement a more robust synchronization mechanism to handle conflicts between online and offline data.

To get started with this project:

1. Set up a new Next.js project: npx create-next-app@latest
2. Install necessary dependencies: npm install idb
3. Copy the provided code into the appropriate files in your project structure.
4. Run the development server: npm run dev

Remember to handle error cases, add proper validation, and implement security measures, especially when dealing with financial data. This example provides a starting point, but a production-ready billing app would require much more extensive development and testing.

I'll modify the billing app to use Indian Rupee (₹) as the default currency. We'll update the relevant components to display and handle amounts in Indian Rupees.

These changes will set Indian Rupee (₹) as the default currency in your billing app. Here's a summary of the modifications:

1. Updated the InvoiceForm to display the ₹ symbol before the amount input.
2. Modified the InvoiceList to use a currency formatter for displaying amounts.
3. Added a currency formatter function in the BillingApp component using the 'en-IN' locale and 'INR' currency.
4. Updated the main page to include Indian-specific branding.

To further enhance the app for the Indian market, consider adding these features:

1. GST (Goods and Services Tax) calculation and reporting
2. Integration with popular Indian payment gateways (e.g., Razorpay, PayTM)
3. Support for multiple languages, including Hindi and other regional languages
4. Compliance with Indian financial regulations and tax laws
5. Integration with Indian accounting software (e.g., Tally)
6. Support for generating invoices in formats compliant with Indian tax regulations

Remember to consult with a legal expert or accountant familiar with Indian tax laws to ensure your app complies with all relevant regulations for billing and invoicing in India.