There exist a co-ordinate system from chromosomes like "12p11.3". In this system, first integer range from 1 to 23 i.e it takes homologous chromosomes as a pair. If we want to distinguish among homologous chromosomes, how do we refer to each on of the pair? Is it possible to determine if one chromosome from a pair of homologous chromosomes is from father or mother?
The cytogenetic notation seems to refer to parts of the chromosome when they're being karyotyped when the chromsomes are condensed in metaphase. If so, I think you might be able to use FISH to look for pieces of maternal or paternal genetic content on the chromosome. It looks like you can use
It is not possible to know in most cases whether a chromosome is maternal or paternal without knowing the genome sequence of both mother and father (with some additional effort; see below).
There are certain exceptions and these include chromosomes that bear imprinted genes. For example H19 gene on chromosome-1 is maternally imprinted i.e. the paternal copy is silenced by DNA methylation. Likewise there are many imprinted genes; a list of imprinted genes could be found here.
A technique called bisulphite sequencing (also MeDIP-seq) can be used to find methylated regions in the genome but to map chromosomes using this methylation information is not straightforward. You have to do either of these two:
With X-chromosome it is possible to find out which one is paternal in relatively easy way but this check has to be done at neonatal stage (when placenta is still present). See this post.