Publishing on your custom domain requires one-time support from your developer to create a new DNS record for the blog subdomain in the DNS manager of your domain provider, as elaborated in this article.
1Open the page editor of the page which has to be published. Click on the "Publish" button on the top right.
2 In the sidebar that opens, click on the Publish Type dropdown and choose "Custom Domain".
3 Enter the subdomain name as desired for your blog page. Create a new DNS record for this blog subdomain in the DNS manager of your domain provider. Refer to this article for more details.
4 Click on "Save and Publish".