Is there a way that we could backup the database in number of smaller parts or change the backup path? Regards to this question that I had asked a day ago I want to know if there is any way that I could take the database backup in the number of smaller parts.

Or 
If there is any way that I could change the database backup path to my local drive.

I am connecting to remote through Microsoft SQL Server Management Studio 2017.
Sure - Have a look at Backup to multiple files for faster and smaller SQL Server files.

Problem

Have you ever wished you could get your backups to run faster? Well there may be a way, by writing to multiple files. Creating SQL Server backups is pretty simple to do; you can use the SQL Server management tools or you can use T-SQL commands to issue the backup. But sometimes with large databases it takes a long time to run and it is difficult to copy this very large file across the network or even to your backup tapes.

Solution

Write your database backup to multiple files. In addition to writing your database backup to one file you have the ability to write to multiple files at the same time and therefore split up the workload. The advantage to doing this is that the backup process can run using multiple threads and therefore finish faster as well as having much smaller files that can be moved across the network or copied to a CD or DVD. Another advantage to writing to multiple files is if you have multiple disk arrays you can write your backup files to different arrays and therefore get better I/O throughput. One thing to note is that to maintain the I/O throughput you should keep the writing of your backup files and the reading of the database file on different disk arrays.

Backup to multiple files using T-SQL

BACKUP DATABASE [Northwind] TO 
DISK = 'C:\Northwind_file1.bak', 
DISK = 'D:\Northwind_file2.bak', 
DISK = 'E:\Northwind_file3.bak', 
DISK = 'F:\Northwind_file4.bak' 
WITH INIT , NOUNLOAD , NAME = 'Northwind backup', NOSKIP , STATS = 10, NOFORMAT


In reference to your question 


  Or If there is any way that I could change the database backup path to
  my local drive.


It's important to note that when you are running backups against a particular SQL Server instance, the backup drives you use in the BACKUP command are drives known by the server that the SQL Server instance is running on.  Now, you could also use a fileshare (assuming you have the proper permissions to write to it).  As far as writing to your local drive, you might be able to achieve that if you create a fileshare on your computer and use that fileshare in your BACKUP command.

I ran a quick BACKUP on one of our 100+gb play databases using 4 backup files.  It appears that BACKUP certainly tried to divide the data as evenly as possible.



An important reminder is


  All of the files must be available, and all must be referenced in a
  restore session.


Some additional valuable information can be found at Improving the Performance of Backups