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Filters menu > Shadows and Glows
There are a few choices there which you might want to try out. Also, if you find a filter that's close to what you want, but you want to change something about it, such as the color of the glow, or the intensity, or whatever; there is a way to do that. Just let us know what kind of change you want to make and we can tell you how.
Are your questions about the stroke separate from the question about the filters? If you want to apply the filter only to the stroke, then you'll need to make the stroke a separate object (duplicate the text, and remove the fill, also remove the stroke from the original). If you want the filter to only be applied to the middle, inner or outer part of the stroke.....that might be tricky. I guess it would have to be a pretty wide stroke, or else it would be hard to really see the difference.
However, I'm thinking your question about the stroke is separate from the filter question. As far as I know, Inkscape doesn't have an option for whether the stroke is aligned from the middle, inner or outer edge, although it's a long time requested feature. There are ways to achieve the appearance of a stroke being aligned this way or that, but not by actually using a stroke. You'd have to use a regular path. We can show you how, if you like. Hhmm....actually it might be possible to do it with a stroke, but the stroke would be a separate object from the fill.
Inkscape uses a middle alignment.
There are options for the z-order of strokes, fills and markers. So you might be able to sort of fake the stroke alignments using z-order, depending what you want.
And your last question, "no overlapping stroke". Do you mean you want the stroke to be aligned from its inner edge? Or do you mean you don't want any stroke at all?