I can see the following field types as default in share-point 2013, 
But, I want to create a custom field type here, for the example consider 'slider' is a new field that is available after 'Managed Metadata', So What i want to do?
If you are using SharePoint 2007/2010, you can inherit from OOB field types and create a new field type. Following articles can help you get started:
http://msdn.microsoft.com/en-us/library/office/bb861799(v=office.14).aspx http://weblogs.asp.net/sreejukg/archive/2012/02/05/developing-custom-field-type-for-sharepoint-2010.aspx
If you are using SharePoint 2013, you can create custom fields using a new technique called client-side rendering.
With SharePoint 2013, we can modify the presentation and validation of a custom field (or technically any field) on any form in SharePoint as well as in Views simply via JavaScript. This is an incredibly powerful capability. It provides a nice, easy, standard (and supported) way of customizing the end user experience to be more efficient and friendly.
References:
http://blog.aptillon.com/2012/10/12/custom-field-types-in-sharepoint-2013-apps/ http://code.msdn.microsoft.com/office/SharePoint-2013-Create-eb30a620 http://spdevlab.com/2013/06/09/custom-field-type-for-sharepoint-2013-visa-card-field-sample/
It depends, deploying custom field types is not supported for SharePoint Online.
According to MSDN:
Only fields that use a built-in SharePoint Foundation field type, or a custom field type that is previously installed in a farm solution, are possible. A custom field type cannot be deployed in a sandboxed solution.
Custom field types could be deployed as a farm solution only since field type definitions require a fldtype*.xml file to be deployed to the hive.
Instead of creating custom field type, you could reuse existing field type, for example Number field type and then
Please follow this article as an introductory to CSR and how to customize the rendering of a field.