Repl;acement fusible links

Did you check power an grounds at the alternator ? The heavy gage wire on the back of the alternator should have B+ voltage , if not fusible link is blown . The connector ,pin's 1 & 3 should have B+ voltage also . There are videos on youtube on checking charging systems . Do you know how to do automotive electrical testing ? How to use a DVOM - digital volt ohm meter ?
How to Test an Alternator Diagnose Charging Issues

Yes, I believe that would be a fusible link, rather than a large fuse (maxi-fuse) used on later models. The fusible links will tie into the positive battery cable somewhere. If not at the battery, then look for them where the positive cable connects to the starter. A bad fusible link will look like some of the insulation melted, may have bumps and bulges where the fusible link blew out. To replace a link, you cut it out and solder in a new link of the same rating.

There are at least two, and maybe three Fusible Links just off the battery on white wires. You probably blew them out. They can be cut out and replaced. One is a 60 amp fuse link, designated AM1-it is for power to the ignition switch. Another fuse link will go to the alternator. You need to check them all.
A parts store can probably find the correct replacements. If not, go to the dealer's parts place.
When a fusible link blows, the wire insulation may be partially melted, the wire may look and feel like it has bulges. They are about 3 inches long. You cut the wire before and after them, and solder in a new fuse link. Take the old bad ones with you to get the proper replacement.

Clip the wire on both ends of the fusable link then and new fuse

there are 2 types of fusible links. One is a wire and the other is more like a fuse (a short wire in a small box with a clear window. They are used to protect high current components. I see you have a couple of the old style wire types in your starter circuit. Tell the parts guy which one you need--is it starter to battery or starter to alternator, etc. There is no amperage specified on the diagram, but the parts chain may have better info on what you will need. I have pasted examples below.

I know that fusible links on GM cars come directly off of the starter positive terminal. They can be identified by looking for a cylindrical (3/4" long by 1/2" in diameter) barrel of plastic on a colored piece of wire. If the technician pulls on a fusible link which is about 8" long (replacement), then the wire insulation will stretch by about 1" to 3" indicating the wire inside has broken.
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I looked up fusible link on the 1999 Dodge Ram and came up with this information which is a little bit different as far as form factor:

Fusible Links Removal & Installation All Engines To Remove:
NOTE: If a generator cartridge fuse fails, be certain to inspect and test the vehicle charging system before replacing the cartridge fuse and returning the vehicle to service.

1. Before servicing the vehicle refer to the precautions at the beginning of this section.
2. Remove or disconnect the following:
   • The negative battery cable
   • The cover from the Power Distribution Center (PDC)
   • The two screws securing the generator cartridge fuse to the two B(+) terminal stud bus bars within the PDC
   • The generator cartridge fuse from the PDC

To Install:

1. Install or connect the following:
   • The generator cartridge fuse onto the two B(+) terminal stud bus bars within the PDC
   • The two screws securing the generator cartridge fuse to the two B(+) terminal stud bus bars within the PDC
   • Tighten the screws
     1. Torque to: 30 in. lbs. (3.4 Nm)
     NOTE: Ensure that both screws are tightened to the proper torque values.
     
   • The cover onto the PDC
   • The negative battery cable

if just the starter fusible link is burned then you should have power to and from the switch, and also power before but not after the fusible link itself. if this is the case you may actually have a bad starter. fusible links burn out for a reason. of course, you'd have to replace the burned fusible link as well.

It called a Fusible Link. There is no fixing a Fusible Link, it has to be replaced.

the main fusable links are located at the main post on the starter

There should be two small 8mm bolts holding the fusible link by the sides...don't pull the fusible link before unscrewing the 2 bolts as they will damage the holder.
cheers