%Data_Hash = (
    Call_Hash => {
            TST_IDS_Large_1 =>2.9E-12,
            TST_IDS_Large_2 =>1.85E-12,

            TST_IDS_Small_1 =>1.86E-9,
            TST_IDS_Small_2 =>2.83E-9,
        },
    OPT_VGS_1 =>0,
    OPT_VGS_2 =>0.02,
    
);
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{key1 => val1, key2 => val2} returns a scalar pointer to a hash with the key value pairs listed. In order to interact with it, your code would read:

@idlarge = ($Data_Hash{Call_Hash}{"TST_" . "IDS_Large_1"}, $Data_Hash{Call_Hash}{"TST_" . "IDS_Large_2"}, ...)

or

@idlarge = ($Data_Hash{Call_Hash}->{"TST_" . "IDS_Large_1"}, $Data_Hash{Call_Hash}{"TST_" . "IDS_Large_2"}, ...)

since consecutive indices contain an implicit deference.

Update: I misunderstood the spec. Assuming that your access methods are correct, you actually want two completely separate hashes. The values of %Call_Hash are being used as keys in the %Data_Hash. The data structures you want are given by:

%Data_Hash = (
    OPT_VGS_1 =>0,
    OPT_VGS_2 =>0.02,
);
%Call_Hash = (
    TST_IDS_Large_1 =>2.9E-12,
    TST_IDS_Large_2 =>1.85E-12,

    TST_IDS_Small_1 =>1.86E-9,
    TST_IDS_Small_2 =>2.83E-9,
);
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except that the values of %Call_Hash should correspond to keys in %Data_Hash.

A good place to start is the perlreftut documentation - a tutorial on Perl references.

%Data_Hash = (
    'Call_Hash' => {
            TST_IDS_Large_1 =>2.9E-12,
            TST_IDS_Large_2 =>1.85E-12,

            TST_IDS_Small_1 =>1.86E-9,
            TST_IDS_Small_2 =>2.83E-9,
        },
    'OPT_VGS_1' => 0,
    'OPT_VGS_2' => 0.02,
    
);
[download]

There are a couple of things that will help with this sort of problem:

Always use strictures (use strict; use warnings;). They give an early warning about things going pear shaped and often provide the right information to figure out what the nature of the problem is.

Data::Dump::Streamer or Data::Dumper provide really useful ways of visualizing complicated data structures.

Of course reading the documentation that others have suggested will help a great deal too. Managing interesting data structures is at least as important to attaining Perl proficiency as knowing how to use Perl's regular expressions.

The essential difficulty in perl is, you can represent the same datastructure in a reference form (eg \%Hash) and in (what I call) a list form (eg %Hash). For nesting you need references, because lists are flattened:

(1,(2,3)) is nothing else then (1,2,3)

but (1,[2,3]) is a list with a literal reference to an array as second element.

As mentioned above better also have a look into perlreftut

What do you mean with I have no control over the call.?

You are not "calling" anything in your code.

CountZero

A program should be light and agile, its subroutines connected like a string of pearls. The spirit and intent of the program should be retained throughout. There should be neither too little or too much, neither needless loops nor useless variables, neither lack of structure nor overwhelming rigidity." - The Tao of Programming, 4.1 - Geoffrey James

%Call_Hash = (
    TST_IDS_Large_1 =>"OPT_VGS_1",
    TST_IDS_Large_2 =>"OPT_VGS_2",
    TST_IDS_Small_1 =>"OPT_VGS_3",
    TST_IDS_Small_2 =>"OPT_VGS_4"
);

%Data_Hash = (
    OPT_VGS_1 =>0,
    OPT_VGS_2 =>0.02,
    OPT_VGS_3 =>0.04,
    OPT_VGS_4 =>0.08    
);
[download]